Exhibit 99.1

Contacts:

Maxim Pharmaceuticals	Burns McClellan
Larry G. Stambaugh	Jonathan M. Nugent
Chairman & Chief Executive Officer	(212) 213-0006

John D. Prunty
Chief Financial Officer

(858) 453-4040

MAXIM PHARMACEUTICALS ANNOUNCES
2005 SECOND QUARTER FINANCIAL RESULTS

SAN DIEGO, Calif., May 2, 2005 — Maxim Pharmaceuticals, Inc. (Nasdaq NM: MAXM, SSE: MAXM) today announced results for the quarter ended March 31, 2005, the second quarter of its fiscal year. The net loss applicable to common stock for the quarter totaled $6.6 million or $0.23 per share, compared to a net loss applicable to common stock of $8.9 million or $0.32 per share, for the prior-year quarter.

The net loss applicable to common stock for the six months ended March 31, 2005 totaled $16.2 million or $0.57 per share, compared to a net loss applicable to common stock of $18.8 million or $0.67 per share for the same period in the prior year. The decrease in the net loss for the period resulted primarily from a decrease in Research and Development expense resulting from the wind-down of the Company’s Ceplene™ clinical trials and a reduction in expenses resulting from the October 2004 and February 2005 work force reductions.

The Company had cash, cash equivalents and investments totaling $32.6 million at March 31, 2005. Maxim used net cash of $7.3 million in its operations during the quarter ended March 31, 2005.

“During the quarter we further realigned our resources with our corporate objectives,” said John D. Prunty, Maxim’s Chief Financial Officer. “Our apoptosis modulator platform continues to progress and we were pleased to recently announce the achievement of a $1.0 million development milestone under an agreement with Myriad Genetics based on the dosing of the first

patient in a Phase 1 clinical program. We also continue to work with Piper Jaffray & Co. to identify and evaluate our strategic options.”

Maxim Overview

Maxim Pharmaceuticals is a biopharmaceutical company dedicated to developing innovative cancer therapeutics. Maxim’s lead drug candidate is Ceplene™ (histamine dihydrochloride), which has shown a statistically significant improvement in leukemia free survival in a Phase 3 clinical trial as a remission maintenance therapy for patients with acute myeloid leukemia (AML). Maxim is currently seeking a strategic partnership to complete commercialization and further development of Ceplene in AML and other indications. Maxim is also discovering and developing small-molecule apoptosis inducers to treat cancer using its proprietary high-throughput screening technology and its chemical genetics approach. This program has identified four lead oncology candidates that are proceeding to clinical trials independently and through collaborations.

Apoptosis compounds and Ceplene are investigational drugs and have not been approved by the U.S. Food and Drug Administration or any international regulatory agency.

This news release contains certain forward-looking statements that involve risks and uncertainties. Such forward-looking statements include statements regarding attempts to identify new strategic opportunities which may include a strategic transaction, the efficacy, safety and intended utilization of the Company’s apoptosis compounds and Ceplene, the conduct and results of the Company’s clinical trials, and the Company’s plans regarding regulatory filings, future research and clinical trials and plans regarding partnering activities. Such statements are only predictions and the Company’s actual results may differ materially from those anticipated in these forward-looking statements. Factors that may cause such differences include the risk that the Company may not be able to identify acceptable strategic opportunities or conclude any strategic transaction which it does identify, the risks associated with the Company’s diminishing cash resources and reliance on outside financing to meet is capital requirements, the risk that products that appeared promising in early research and clinical trials do not demonstrate safety or efficacy in larger-scale or later clinical trials, the risk that the Company will not obtain approval to market its products, and the risks associated with the Company’s reliance on collaborative partners for further clinical trials, development and commercialization of product candidates. These factors and others are more fully discussed in the Company’s periodic reports and other filings with the Securities and Exchange Commission

Note: The Maxim logo is a trademark of Maxim.

Editor’s Note: This release is also available on the Internet at http://www.maxim.com.

MAXIM PHARMACEUTICALS, INC.

CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS (Unaudited)

(in thousands, except share and per share amounts)

	Three Months Ended March 31						Six Months Ended March 31
	2005			2004			2005			2004

Collaboration and research revenue	$	1,120		$	1,273		$	1,483		$	2,692

Operating expenses:
Research and development	5,119			8,363			12,068			17,694
Business development and marketing	482			647			1,464			1,290
General and administrative	1,985			1,589			4,200			3,355
Provision for note receivable from officer	324			—			324			—
Total operating expenses	7,910			10,599			18,056			22,339

Loss from operations	(6,790		)	(9,326		)	(16,573		)	(19,647		)

Other income (expense):
Investment income	163			407			371			877
Interest expense	(10		)	(20		)	(24		)	(43		)
Other income (expense)	(1		)	—			1			3
Total other income	152			387			348			837

Net loss applicable to common stock	$	(6,638	)	$	(8,939	)	$	(16,225	)	$	(18,810	)

Basic and diluted net loss per share of common stock	$	(0.23	)	$	(0.32	)	$	(0.57	)	$	(0.67	)

Weighted average shares outstanding	28,599,419			28,034,279			28,580,045			28,010,377

SELECTED BALANCE SHEET INFORMATION (Unaudited)

	March 31, 2005			September 30, 2004

ASSETS
Cash, cash equivalents and investments	$	32,625		$	52,904
Total assets	42,868			64,185
Long-term liabilities	13			96
Stockholders’ equity	37,261			53,399

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Maxim Pharmaceuticals

Burns McClellan

MAXIM PHARMACEUTICALS ANNOUNCES 2005 SECOND QUARTER FINANCIAL RESULTS

MAXIM PHARMACEUTICALS ANNOUNCES
2005 SECOND QUARTER FINANCIAL RESULTS

MAXIM PHARMACEUTICALS INC 8-K