Exhibit 99.1

FORM OF

INSTRUCTIONS AS TO USE OF SUBSCRIPTION RIGHTS STATEMENTS

DELCATH SYSTEMS, INC.

Please consult D.F. King & Co., Inc., the Information Agent for the Rights Offering,

or your bank or broker as to any questions.

The following instructions relate to a rights offering (the “Rights Offering”) by DELCATH SYSTEMS, INC., a Delaware corporation (“DCTH” or the “Company”), to the holders of record, on August 3, 2018, of its common stock, $0.01 par value (the “Common Stock”) and its warrants, as described in DCTH’ prospectus dated [ ], 2018 (the “Prospectus”). On August 3, 2018 (the “Record Date”), each holder of record of Common Stock and warrants at the close of business will receive, at no charge, 500 non-transferable subscription righst (the “Subscription Rights”) for each share of Common Stock and each share of Common Stock into which warrants are exercisable that are held at the Record Date.

Pursuant to the Rights Offering, the Company is issuing Subscription Rights to subscribe for up to $50 million in Common Stock on the terms and subject to the conditions described in the Prospectus. Each subscription right will entitle the holder to purchase one share of Common Stock, which we refer to as the basic subscription right, at a subscription price per share equal to $1.75 (“Subscription Price”). In the event that holders exercise Subscription Rights for in excess of the maximum exercise amount, which is the lesser of $50.0 million or 28,571,429 shares of our Common Stock (not including the Over-Subscription Privilege), the amount subscribed for by each person will be proportionally reduced, based on the amount subscribed for by each person (not including any Over-Subscription Privilege subscribed for).

We will not issue fractional shares of Common Stock in the Rights Offering. Any excess subscription payments received by the Subscription Agent will be returned as soon as practicable after Expiration Date of the Rights Offering, without interest or penalty.

The Subscription Rights will expire at 5:00 PM Eastern Time, on August 27, 2018, unless extended (“the “Expiration Date”). If you do not exercise your Subscription Rights before that time, your Subscription Rights will expire and will no longer be exercisable. DCTH will not be required to issue shares to you if Securities Transfer Corporation (the “Subscription Agent”), receives your Subscription Rights Statement or your subscription payment after that time. DCTH has the option to extend the Rights Offering in its sole discretion, although it does not presently intend to do so. DCTH may extend the Rights Offering by giving oral or written notice to the Subscription Agent before the Expiration Date. If DCTH elects to extend the Rights Offering, DCTH will issue a press release announcing the extension no later than 9:00 AM Eastern Time, on the next business day after the most recently announced Expiration Date of the Rights Offering.

The number of Subscription Rights to which you are entitled is printed on the face of your Subscription Rights Certificate. You should indicate your wishes with regard to the exercise of your Subscription Rights by completing the appropriate section on the back of your Subscription Rights Certificate and returning the Subscription Rights Certificate with your payment to the Subscription Agent in the envelope provided.

YOUR SUBSCRIPTION RIGHTS STATEMENT MUST BE RECEIVED BY THE SUBSCRIPTION AGENT ON OR BEFORE THE EXPIRATION DATE AND TIME. PAYMENT OF THE SUBSCRIPTION PRICE OF ALL SUBSCRIPTION RIGHTS EXERCISED, INCLUDING SUBSCRIPTION RIGHTS PURSUANT TO THE OVER-SUBSCRIPTION PRIVILEGE, MUST BE RECEIVED BY THE SUBSCRIPTION AGENT ON OR BEFORE THE EXPIRATION DATE AND TIME. ONCE YOU EXERCISE YOUR SUBSCRIPTION RIGHTS, YOU CANNOT REVOKE THE EXERCISE OF SUCH SUBSCRIPTION RIGHTS. SUBSCRIPTION RIGHTS NOT VALIDLY EXERCISED PRIOR TO THE EXPIRATION DATE OF THE RIGHTS OFFERING WILL EXPIRE. IN CASE YOU HOLD SUBSCRIPTION RIGHTS THROUGH A BROKER OR OTHER NOMINEE, YOU SHOULD VERIFY WITH YOUR BROKER OR NOMINEE BY WHEN YOU MUST DELIVER YOUR INSTRUCTION.

1. Subscription Rights. To exercise Subscription Rights, complete your Subscription Rights Certificate and send your properly completed and executed Subscription Rights Certificate, together with payment in full of the Subscription Price for each share of Common Stock subscribed for pursuant to the Basic Subscription Right and the Over-Subscription Privilege, to the Subscription Agent. PLEASE DO NOT SEND SUBSCRIPTION RIGHTS STATEMENTS OR PAYMENTS TO DCTH. The method of delivery of the Subscription Rights Certificate and the payment of the Subscription Price to the Subscription Agent is at your election and risk. Subscription Rights Certificates and payments must be received by the Subscription Agent prior to the Expiration Date and Time. If you send your Subscription Rights Certificate and payment by mail, then they should be sent by registered mail, to arrive before the Expiration Date. If more shares of Common Stock are subscribed for pursuant to the Over-Subscription Privilege than are available for sale, additional shares of Common Stock will be allocated pro rata among holders, as described in the Prospectus. The Subscription Rights are non-transferable, and may not be sold, transferred, assigned or given away to anyone.

2. Acceptance of Payments. Payments will be deemed to have been received by the Subscription Agent only upon the (i) receipt of a cashier’s check drawn against a U.S. bank payable to “American Stock Transfer & Trust Company, LLC, as Subscription Agent for DELCATH SYSTEMS, INC.,” or (ii) receipt of a wire transfer of immediately available funds directly to the account maintained by American Stock Transfer & Trust Company, LLC, as subscription agent, for purposes of accepting subscriptions in this rights offering at JPMorgan Chase Bank, 55 Water Street, New York, New York 10005, ABA #021000021, Account # 530-354616 American Stock Transfer FBO Delcath Systems, Inc./[shareholder name as it appears on face of certificate].

3. Contacting the Subscription Agent or Information Agent. The address of the Subscription Agent is shown below. Delivery to an address other than shown below does not constitute valid delivery.

By Mail, Hand or Overnight Courier

American Stock Transfer & Trust Company, LLC

Operations Center

Attn: Reorganization Department

6201 15th Avenue

Brooklyn, New York 11219

If you have other questions or need assistance, please contact the Information Agent for the Rights Offering:

D. F. King & Co., Inc.

48 Wall Street, 22nd Floor

New York, New York 10005

Banks and Brokers call: (212) 269-5550

All others call toll-free: (877) 732-3612

Email: DCTH@dfking.com

4. Partial Exercises; Effect of Over-Payments and Under-Payments. If you exercise less than all of the Subscription Rights evidenced by your Subscription Rights Certificate, and make the choice to submit an additional exercise request you must contact the Information Agent for a new Subscription Rights Certificate. If you choose to have a new Subscription Rights Certificate sent to you, you may not receive any such new Subscription Rights Certificate in sufficient time to permit exercise of the Subscription Rights evidenced thereby. You will not be able to rescind their subscription. If you do not indicate the number of shares of Common Stock to be subscribed for on your Subscription Rights Certificate, or if you indicate a number of shares of Common Stock that does not correspond with the aggregate Subscription Price payment you delivered, you will be deemed to have subscribed for the maximum number of shares of Common Stock that may be subscribed for, under both the Basic Subscription Right and the Over-Subscription Privilege, for the aggregate Subscription Price you delivered. If the Subscription Agent does not apply your full Subscription Price payment to your purchase of Common Stock, then the

Subscription Agent will return the excess amount to you, without interest or deduction, as soon as practicable after the Expiration Date. If you subscribe for fewer than all of the shares of Common Stock represented by your Subscription Rights Certificate, then the unexercised Subscription Rights will become null and void on the Expiration Date.

5. Deliveries to Holders. The following deliveries and payments to you will be made to the address shown on the face of your Subscription Rights Certificate:

(a) Basic Subscription Right. The shares of Common Stock that are purchased pursuant to the valid exercise of Basic Subscription Rights will be issued in book-entry, or uncertificated, form meaning that you will receive a direct registration (DRS) account statement from our transfer agent reflecting ownership of these shares if you are a holder of record of Common Stock. The Subscription Agent will arrange for the issuance of the Common Stock as soon as practicable after the expiration of the Rights Offering, payment for the shares of Common Stock subscribed for has cleared, and all prorating calculations and reductions contemplated by the terms of the Rights Offering have been effected. If you hold your shares of Common Stock in the name of a custodian bank, broker, dealer, or other nominee, DTC will credit your account with your nominee with the shares you purchased in the Rights.

(b) Over-Subscription Privilege. The shares of Common Stock that are purchased pursuant to the valid exercise of Over-Subscription Privileges to purchase additional shares of Common Stock will also be issued in book-entry, or uncertificated, form meaning that you will receive a direct registration (DRS) account statement from our transfer agent reflecting ownership of the Common Stock if you are a holder of record of Common Stock. The Subscription Agent will arrange for the issuance of the Common Stock as soon as practicable after the Expiration Date of the Rights Offering, payment for the shares of Common Stock subscribed for has cleared, and all prorating calculations and reductions contemplated by the terms of the Rights Offering have been effected. If you hold your shares of Common Stock in the name of a custodian bank, broker, dealer, or other nominee, DTC will credit your account with your nominee with the shares of Common Stock you purchased in the Rights.

(c) Excess Payments. If you exercised your Over-Subscription Privilege and are allocated less than all of the shares of Common Stock for which you wished to over-subscribe, then your excess Subscription Price payment for shares of Common Stock that were not allocated to you will be returned by the Subscription Agent to you, without interest or deduction, as soon as practicable after the Expiration Date.

6. Execution.

(a) Execution by Registered Holder. The signature on the Subscription Rights Certificate must correspond with the name of the registered holder exactly as it appears on the face of the Subscription Rights Certificate without any alteration or change whatsoever. Persons who sign the Subscription Rights Certificate in a representative or other fiduciary capacity must indicate their capacity when signing.

(b) Execution by Person Other Than Registered Holder. If the Subscription Rights Certificate is executed by a person other than the holder named on the face of the Subscription Rights Certificate, YOU MUST SIGN IN YOUR LEGAL CAPACITY WITH YOUR SIGNATURE MEDALLION GUARANTEED. YOUR GUARANTOR (BANK/BROKER) WILL REQUIRE PROOF OF YOUR AUTHORITY TO ACT. CONSULT YOUR GUARANTOR FOR THEIR SPECIFIC REQUIREMENTS. YOU OR YOUR GUARANTOR MAY ACCESS THE SECURITIES TRANSFER ASSOCIATION (STA) RECOMMENDED REQUIREMENTS ON-LINE AT www.stai.org.

7. Method of Delivery. The method of delivery of Subscription Rights Certificates and payment of the Subscription Price to the Subscription Agent will be at the election and risk of the Subscription Rights holder. If sent by mail, it is recommended that they be sent by registered mail, with return receipt requested, and that a sufficient number of days be allowed to ensure delivery to and receipt by the Subscription Agent prior to the Expiration Date.

8. No Revocation. If you exercise any of your Basic Subscription Rights or Over-Subscription Privilege, you will not be permitted to revoke or change the exercise or request a refund of monies paid. You should not exercise your Subscription Rights unless you are sure that you wish to purchase Common Stock. Once you exercise your Subscription Rights, you cannot revoke the exercise of such Subscription Rights even if you later learn information that you consider to be unfavorable and even if the market price of our Common Stock is below the Subscription Price.

9. Special Provisions Relating to the Exercise of Subscription Rights through the Depository Trust Company. In the case of Subscription Rights that are held of record through The Depository Trust Company (“DTC”), exercises of the Subscription Rights may be effected by instructing DTC to transfer Subscription Rights from the DTC account of such holder to the DTC account of the Subscription Agent, together with certification as to the aggregate number of Subscription Rights exercised pursuant to the Subscription Right by each beneficial owner of Subscription Rights on whose behalf such nominee is acting, and payment of the Subscription Price for each share of Common Stock subscribed for. Banks, brokers and other nominee holders of Subscription Rights who exercise the Basic Subscription Right and the Over-Subscription Privilege on behalf of beneficial owners of Subscription Rights will be required to certify to the Subscription Agent and DCTH as to the aggregate number of Subscription Rights that have been exercised, and the number of shares of Common Stock that are being subscribed for pursuant to the Over-Subscription Privilege, by each beneficial owner of Subscription Rights (including such nominee itself) on whose behalf such nominee holder is acting. In the event such certification is not delivered in respect of a Subscription Rights Certificate, the Subscription Agent shall for all purposes (including for purposes of any allocation in connection with the Over-Subscription Privilege) be entitled to assume that such Statement is exercised on behalf of a single beneficial owner.

FOR QUESTIONS REGARDING THE RIGHTS OFFERING, ASSISTANCE REGARDING THE METHOD OF EXERCISING SUBSCRIPTION RIGHTS OR FOR ADDITIONAL COPIES OF RELEVANT DOCUMENTS, PLEASE CONTACT D.F. KING & CO. INC., AT BANKS AND BROKERS CALL: (212) 269-5550, ALL OTHERS CALL TOLL-FREE: (877) 732-3612, EMAIL: DCTH@DFKING.COM.

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