Exhibit 10.1

AGREEMENT

This Agreement (the “Agreement”) is dated as of July 23, 2015, by and among Real Estate Strategies L.P., a Bermuda Limited Partnership (“RES) IRSA Inversiones y Representaciones Sociedad Anónima, an Argentine sociedad anónima (“IRSA”) and Condor Hospitality Trust, Inc., a corporation (the “Company” and, together with the Investor and IRSA, the “Parties” and any of them individually, a “Party”).

WHEREAS, the Company is planning an exchange offer of up to 11,664,615 shares of its common stock for its Series A preferred stock and Series B preferred stock and which it contemplates will result in the issuance of in excess of 20% of its common stock (the “Exchange Offer”);

WHEREAS, pursuant to Section 7(c) of the terms of the 6.25% Series C convertible preferred stock, the consents of RES and IRSA are required for the Company to issue in excess of 20% of its common stock in the Exchange Offer;

WHEREAS, the Company believes the success of the Exchange Offer would be enhanced by the conversion of some or all of its shares of Series C convertible preferred stock into common stock pursuant to the terms of the Series C convertible preferred stock;

NOW, THEREFORE, in consideration of the foregoing and the mutual agreements set forth herein, and other good and valuable consideration, the receipt and adequacy of which is hereby acknowledged, the Parties, intending to be legally bound, hereby agree as follows:

1. Consent to Exchange Offer.

RES and IRSA hereby consent to the issuance of common stock by the Company pursuant to the Exchange Offer. The consent by RES and IRSA is exclusively for the Exchange Offer and not for any other offering or matter.

2. Conditional Agreement to Convert Series C Convertible Preferred Stock.

(a) Conversion. RES and IRSA agree that they shall cause the Series C convertible preferred stock to be converted into common stock pursuant to the terms, provided:

(i) Minimum Acceptance—at least 80% of the shares of each of the Series A preferred stock and the Series B preferred stock are tendered and exchanged for common stock in the Exchange Offer (the “Minimum Acceptance”);

(ii) Shareholder Approvals—the requisite vote of Company shareholders is received at or prior to the consummation of the Exchange Offer approving (the “Shareholder Approvals”):

(iii) Conditional Agreements—the Company complies with its conditional agreements set forth in Sections 3 and 4 below.

(b)(i) Amount of Conversion. If the foregoing conditions of Section 2(a) are met, then at the time of the consummation of the Exchange Offer, RES and IRSA shall cause the Series C convertible to be converted at a percentage equal to the percentages of Series A preferred stock and Series B preferred stock tendered and exchanged for common stock in the Exchange Offer. If the Series A preferred stock and Series B preferred stock are each exchanged at 80% or above, but at different percentages, the percent of conversion of the Series C convertible preferred stock above 80% will be the weighted average (based on liquidation value) of the difference in the exchanged percentages of the Series A preferred stock and Series B preferred stock. For example, if 80% of the Series A preferred stock and 90% of the Series B preferred stock are tendered in the exchange offer, then RES would convert 87.2% of the Series C convertible preferred stock.

(ii) Minimum Beneficial Ownership. Notwithstanding the foregoing, RES and IRSA may retain beneficial ownership of 1,000 shares of Series C convertible preferred stock if the conversion would otherwise result in beneficial ownership of less than that number of shares.

3. Conditional Agreements of Company. If RES and IRSA are obligated pursuant to Section 2(b) above to cause the conversion of shares of Series C convertible preferred stock as set forth therein and the Exchange Offer is contemporaneously consummated then the Company agrees:

(a) Unpaid Dividends—that in addition to the issuance of common stock upon conversion of the Series C convertible preferred stock pursuant to the terms thereof, the Company will also issue a number of shares of common stock to the holder of the Series C convertible preferred stock equal to the unpaid dividends, with compounded interest thereon, on the converted shares of Series C convertible preferred stock at the per share value of the common stock used for the Exchange Offer in return for the waiver of such unpaid dividends by the holder of the Series C convertible preferred stock;

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(b) Charter Amendments—to amend the Company charter to:

(i) Beneficial Ownership Limitation—remove the Beneficial Ownership Limitation;

(ii) Series B Required Redemption—remove the Series B Required Redemption; and

(iii) Non-Voting Common Stock—add authorization to issue non-voting convertible common stock; and add the option for Series C convertible preferred stock to be converted into non-convertible common stock and/or common stock, in a mix at the option of the holder.

(c) Warrant Extension—amend the warrants to add the Warrant Extension;

(d) RES and IRSA Consents—that as long as RES has the right to designate two or more directors to the Company board of directors, the following requires the approval of RES and IRSA:

(i) the merger, consolidation, liquidation or sale of substantially all of the assets of the Company;

(ii) the sale by the Company of common stock or securities convertible into common stock equal to 20% or more of the outstanding common stock or voting stock; or

(iii) any Company transaction of more than $120,000 in which any of its directors or executive officers or any member of their immediate family will have a material interest, exclusive of employment compensation and interests arising solely from the ownership of the Company equity securities if all holders of that class of equity securities receive the same benefit on a pro rata basis;

(e) Committee Assignments—that as long as RES has the right to under the Director Designation Agreement dated February 2, 2012 to have appointed an “Investor Designee” (as that term is defined therein) to the Nominating Committee of the Company board of directors, then RES shall have the right to have appointed one Investor Designee to all current and future committees of the Company board of directors (provided the Investor Designee meets the independence requirements if so required under Nasdaq rules);

(f) Preemptive Rights Term—that Section 3(a) of the Investor Rights and Conversion Agreement dated February 1, 2012 will be deemed amended to eliminate the requirement for a combined stake requirement of 1,250,000 shares of common stock (10,000,000 shares prior to the 8-for-1 reverse stock split) and extend the term of Section 3(a) from January 31, 2018 to January 31, 2020;

(g) Approvals—that as long as RES has the right to designate two or more directors to the Company board of directors:

(i) Ownership Limitation Approval—the affirmative vote of the board members designated by RES will be required as part of the vote of the Company board of directors approving an exemption under Article IX, Section 7 of the Company’s Amended and Restated Articles of Incorporation from the “Ownership Limitation” set forth therein, or otherwise such exemption shall not be approved; and

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(ii) Nomination—director nominees nominated by the Nominating Committee of the Company board of directors shall require the affirmative vote of the RES designated director on the committee or they shall not be nominated.

4. Further Agreement. In the event the weighted average trading price per share of the common stock for the three trading days immediately preceding the last trading day of the tender offer period of the Exchange Offer is below $2.00, then in addition to the shares of common stock issued on conversion of the Series C convertible stock and in connection with the unpaid dividends thereon, the Company shall issue additional shares in the conversion equal to 10% of the liquidation value of the shares so converted, with such shares valued at the per share value of the common stock used in the Exchange Offer, subject to approval of the issuance by the Company board of directors provided that, if the Company board of directors does not approve the issuance of such additional common stock then the Company will terminate the Exchange Offer and the agreements set forth in Section 2 and Section 3 hereof will terminate and the Parties will have no obligations thereunder.

5. Miscellaneous.

(a) Amendment. No amendment or waiver of any provision of this Agreement will be effective with respect to any party unless made in writing and signed by an officer of a duly authorized representative of such party.

(b) Waivers. The conditions to each party’s obligations in the Agreement are for the sole benefit of such party and may be waived by such party in whole or in part to the extent permitted by applicable law. No waiver of any party to this Agreement will be effective unless it is in a writing signed by a duly authorized officer of the waiving party that makes express reference to the provision or provisions subject to such waiver.

(c) Counterparts and Facsimile. For the convenience of the parties hereto, this Agreement may be executed in any number of separate counterparts, each such counterpart being deemed to be an original instrument, and all such counterparts will together constitute the same agreement. Executed signature pages to this Agreement may be delivered by facsimile and such facsimiles will be deemed as sufficient as if actual signature pages had been delivered.

(d) Governing Law and Forum. This Agreement shall be governed by, and construed in accordance with, the internal laws of the State of New York without regard to the principles of conflicts of laws. Each of the parties hereto hereby irrevocably consents, to the maximum extent permitted by law, that any action or proceeding relating to this Agreement or the transactions contemplated hereby shall be brought, at the option of the party instituting the action or proceeding, in any court of general jurisdiction in New York County, New York, in the United States District Court for the Southern District of New York or in any state or federal court sitting in the area currently comprising the Southern District of New York. Each of the parties hereto waives any objection that it may have to the conduct of any action or proceeding in any such court based on improper venue or forum non conveniens, waives personal service of any and all process upon it, and consents that all service of process may be made by mail or courier service directed to it at the address set forth herein and that service so made shall be deemed to be completed upon the earlier of actual receipt or ten days after the same shall have been posted or delivered to a nationally recognized courier service. Nothing contained in this shall affect the right of any party hereto to serve legal process in any other manner permitted by law.

(e) Notices. All notices or other communications required or permitted to be given by any party to any other party pursuant to the terms of this Agreement shall be in writing, unless otherwise specified in this Agreement, and if sent to the Investor, shall be delivered to Real Estate Strategies L.P. Clarendon House 2, Church Street, Hamilton HM CX, Bermuda, c/o IRSA Inversiones y Representaciones Sociedad Anónima, Bolívar 108 (C1066AAB), Buenos Aires,

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Argentina, fax no. +54 (11) 4323-7449, Attention: Eduardo S. Elsztain, with copies to and Zang, Bergel & Vines Abogados, Florida 537, 18th Floor, (C1005AAK), Buenos Aires, Argentina, fax no. +54 (11) 5166-7070, Attention: Pablo Vergara del Carril; or if sent to the Company or the Operating Partnership, shall be delivered to Condor Hospitality Trust, Inc., 1800 West Pasewalk Avenue, Suite 200, Norfolk, Nebraska 68701, fax no. (402) 371-4229 Attention: Chief Executive Officer, with a copy to McGrath North Mullin & Kratz, PC LLO, Suite 3700 First National Tower, 1601 Dodge Street, Omaha, Nebraska 68102, fax no. (402) 952-1802, Attention: Guy Lawson. Each party to this Agreement may change such address for notices by sending to the parties to this Agreement written notice of a new address for such purpose.

(f) Captions. The section, paragraph and clause captions herein are for convenience of reference only, do not constitute part of this Agreement and will not be deemed to limit or otherwise affect any of the provisions hereof.

(g) No Third Party Beneficiaries. Nothing contained in this Agreement, expressed or implied, is intended to confer upon any person or entity other than the parties hereto, any benefit right or remedies.

(h) Time of Essence. Time is of the essence in the performance of each and every term of this Agreement.

(i) Successors, Assigns and Transferees. This Agreement and the rights and obligations hereunder shall be binding upon and inure to the benefit of the parties and their respective legal representatives, heirs, legatees, successors, and assigns and any other transferee.

(j) Assignment. This Agreement and the rights and obligations hereunder may not be assigned without the prior written consent of the parties hereto and any purported or attempted assignment or other transfer of rights or obligations under this Agreement without such consent shall be void and of no force or effect.

(k) Expenses; Attorney’s Fees. Each party will be solely responsible for its fees and expenses in connection with this Agreement, including the fees and expenses of their respective attorneys, accountants, investment bankers and consultants. In any action or proceeding brought to enforce any provision of this Agreement, the successful party shall be entitled to recover reasonable attorney’s fees and expenses in addition to any other available remedy.

(l) Authority. Each Party represents that (i) it has full entity power and authority to enter into this Agreement, (ii) the Agreement has been duly authorized, validly executed and delivered, and (iii) the Agreement constitutes the legal, valid, and binding agreement of the Party, enforceable in accordance with its terms.

(m) Severability. In the event that any one or more of the provisions contained herein, or the application thereof in any circumstances, is held invalid, illegal, or unenforceable in any respect for any reason, the validity, legality, and enforceability of any such provision in every other respect and of the remaining provisions contained herein shall not be in any way impaired thereby.

(n) Entire Agreement. This Agreement constitutes the entire agreement, and supersedes all other prior agreements, understandings, representations and warranties, both written and oral, between the parties, with respect to the subject matter hereof.

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be executed and delivered as of the date first above written.

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