<PAGE>   1


                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                -----------------


                                    FORM 10-Q
                   QUARTERLY REPORT UNDER SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934.


         For Quarter Ended March 31, 1999 Commission file number 0-3390
                          ---------------                       -------


                          UNIMED PHARMACEUTICALS, INC.
             ------------------------------------------------------
             (Exact name of registrant as specified in its charter)



            DELAWARE                                         22-1685346
-------------------------------                        ----------------------
(State or other jurisdiction of                          (I.R.S. Employer 
incorporation or organization)                         Identification Number)

2150 E. Lake Cook Rd., Buffalo Grove, Illinois                 60089
----------------------------------------------               ----------
(Address of principal executive offices)                     (Zip Code)

Registrant's telephone number including area code          (847) 541-2525
                                                           --------------



Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15 (d) of the Securities Exchange Act of 1934
during the preceding 12 months (or for such shorter period that the registrant
was required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days: Yes __X__ No _____.

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the close of the period covered by this report:

        Title of each class                    Number of shares outstanding
        -------------------                    ----------------------------
           Common Stock                                 9,056,765
        ($.25 par value)




<PAGE>   2


                   UNIMED PHARMACEUTICALS, INC. AND SUBSIDIARY


<TABLE>
<CAPTION>
                                                                          Page
                                                                         Number
                                                                         ------
<S>                                                                         <C>
PART I.   Financial Information

     ITEM 1.   Financial Statements

                  Consolidated Balance Sheets                                3

                  Consolidated Statements of Operations                      5

                  Consolidated Statements of Cash Flows                      6

                  Notes to Consolidated Financial Statements                 7


     ITEM 2.   Management's Discussion and Analysis of 
                Results of Operations and Financial Condition                9


PART II.  Other Information                                                 13

SIGNATURE PAGE                                                              14
</TABLE>


                                        2


<PAGE>   3

PART I - FINANCIAL INFORMATION

ITEM 1 - FINANCIAL STATEMENTS
UNIMED PHARMACEUTICALS, INC. AND SUBSIDIARY
CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                       March 31,   December 31,
                                                         1999         1998
                                                     -----------   -----------
ASSETS                                               (unaudited)
<S>                                                  <C>           <C>       
Current assets:
  Cash and cash equivalents                          $   914,935   $   621,910
  Short-term investments                               7,440,000     6,865,467
  Receivables:
    Trade                                              3,103,663     3,756,622
    Other                                                135,716       138,152
                                                     -----------   -----------
      Total receivables                                3,239,379     3,894,774

Inventories                                            4,096,830     3,504,772
Prepaid expenses                                         325,910       243,842
                                                     -----------   -----------

      Total current assets                            16,017,054    15,130,765

Equipment and leasehold improvements, at cost          3,065,142     3,045,449
Less accumulated depreciation and amortization         1,834,054     1,757,232
                                                     -----------   -----------
      Net                                              1,231,088     1,288,217

Product rights, net of amortization                    1,462,113     1,495,733
                                                     -----------   -----------

    Total assets                                     $18,710,255   $17,914,715
                                                     ===========   ===========
</TABLE>

          See accompanying notes to consolidated financial statements.

                                        3
<PAGE>   4

ITEM 1 - FINANCIAL STATEMENTS
UNIMED PHARMACEUTICALS, INC. AND SUBSIDIARY
CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                 March 31,     December 31,
                                                                   1999            1998
                                                               -----------     ------------
                                                               (unaudited)
<S>                                                          <C>               <C>
LIABILITIES AND STOCKHOLDERS' EQUITY

Current liabilities:
  Accounts payable                                           $  2,547,975      $  2,786,878
  Accrued and other liabilities                                 2,999,606         3,080,887
  Rebate and chargeback reserve                                 2,211,369         2,763,863
  Deferred research and development revenue, net                1,067,484               ---
  Due to Roxane Laboratories, Inc.                              3,340,992         2,610,590
  Current portion of long-term obligation                         120,000           120,000
                                                             ------------      ------------
    Total current liabilities                                  12,287,426        11,362,218

Long-term obligation                                              520,426           486,488
                                                             ------------      ------------
    Total liabilities                                          12,807,852        11,848,706

Stockholders' equity:
  Common stock, $.25 par value; authorized 30,000,000
   shares; issued: 9,158,812 and 9,105,362, respectively        2,289,704         2,276,341
  Additional paid-in capital                                   28,641,537        28,432,125
  Accumulated deficit                                         (24,541,018)      (24,154,607)
  Accumulated other comprehensive income (Note 2)                  42,180            42,150
                                                             ------------      ------------
                                                                6,432,403         6,596,009
  Less: treasury stock at cost (102,047 shares)                  (530,000)         (530,000)
                                                             -------------     ------------
      Total stockholders' equity                                5,902,403         6,066,009
                                                             ------------      ------------

    Total liabilities and stockholders' equity               $ 18,710,255      $ 17,914,715
                                                             ============      ============
</TABLE>

          See accompanying notes to consolidated financial statements.

                                        4



<PAGE>   5



UNIMED PHARMACEUTICALS, INC. AND SUBSIDIARY
CONSOLIDATED STATEMENTS OF OPERATIONS
THREE MONTHS ENDED MARCH 31, 1999 AND 1998
(Unaudited)

<TABLE>
<CAPTION>
                                                     Three Months Ended
                                                         March 31,
                                                 --------------------------
                                                     1999             1998
                                                     ----             ----
<S>                                              <C>              <C>         
Net sales                                        $ 5,720,588      $ 4,013,622
Cost of sales                                      1,263,718          905,921
                                                 -----------      -----------

Gross profit                                       4,456,870        3,107,701

Operating and administrative expenses              1,142,662          793,756
Sales and marketing expenses                       2,455,540        2,083,905
Research and development expenses, net             1,516,547        2,104,882
                                                 -----------      -----------
Total expenses                                     5,114,749        4,982,543
                                                 -----------      -----------

Loss from operations                                (657,879)      (1,874,842)

Other income (expense):
  Interest income, net                               101,695          198,630
  Other income (expense)                             169,773          (30,709)
                                                 -----------      -----------
Loss before income taxes                            (386,411)      (1,706,921)

Income tax provision                                     ---              ---
                                                 -----------      -----------

Net loss                                         $  (386,411)     $(1,706,921)
                                                 ===========      ===========

Net loss per share:
 Basic                                           $     (0.04)           (0.19)
                                                 ===========      ===========
                                                      
 Diluted                                         $     (0.04)           (0.19)
                                                 ===========      ===========

Weighted average number of common and 
 common equivalent shares outstanding:
 Basic                                             9,011,327        8,937,294
                                                 ===========      ===========
 Diluted                                           9,011,327        8,937,294
                                                 ===========      ===========
</TABLE>

          See accompanying notes to consolidated financial statements.


                                        5


<PAGE>   6


UNIMED PHARMACEUTICALS, INC. AND SUBSIDIARY
CONSOLIDATED STATEMENTS OF CASH FLOWS
THREE MONTHS ENDED MARCH 31, 1999 AND 1998
(Unaudited)

<TABLE>
<CAPTION>
                                                                       Three Months Ended
                                                                           March 31,
                                                                   --------------------------
                                                                       1999          1998
                                                                       ----          ----
<S>                                                                <C>           <C>         
Cash flows used in operations:
Net loss                                                           $ (386,411)   $(1,706,921)
Adjustments to reconcile net loss to net cash
  used in operations:
  Depreciation and amortization                                       110,442        105,118
  Decrease (Increase) in receivables                                  655,395     (2,585,285)
  (Increase) decrease in inventories                                 (592,058)       577,112
  (Increase) decrease in prepaid expenses and other                   (82,068)        98,551
  (Decrease) increase in payables, accrued and other
      liabilities                                                    (872,678)     1,307,036
  Increase (decrease) in due to Roxane Laboratories, Inc.             730,402       (326,410)
                                                                   ----------    -----------
    Net cash used in operating activities                            (436,976)    (2,530,799)

Cash flows (used in) provided by investing activities:
  Capital expenditures                                                (19,693)       (72,126)
  (Purchase) Sale of short-term investments, net                     (574,533)     6,721,125
                                                                   ----------    -----------
    Net cash (used in) provided by investing activities              (594,226)     6,648,999

Cash flows provided by (used in) financing activities:
  Proceeds from issuance of common stock                                  ---         46,475
  Proceeds from exercise of stock options                             222,775            ---
  Payments for product acquisition obligations                         33,938       (791,500)
  Deferred research and development revenues, net                   1,067,484            ---
                                                                   ----------    -----------
    Net cash provided by (used in) financing activities             1,324,197       (745,025)
Effect of exchange rate changes on cash                                    30           (131)
                                                                   ----------    ------------
Increase in cash and cash equivalents                                 293,025      3,373,044
Cash and cash equivalents at beginning of period                      621,910      1,068,279
                                                                   ----------    -----------
Cash and cash equivalents at end of period                         $  914,935     $4,441,323
                                                                   ==========    ===========
</TABLE>

          See accompanying notes to consolidated financial statements.


                                        6


<PAGE>   7


                   UNIMED PHARMACEUTICALS, INC. AND SUBSIDIARY
                   Notes to Consolidated Financial Statements
                                 March 31, 1999
                                   (Unaudited)


NOTE 1

The consolidated financial information herein is unaudited, other than the
Consolidated Balance Sheet at December 31, 1998, which is derived from the
audited financial statements, but does not include all disclosures required by
generally accepted accounting principles. The unaudited interim financial
statements include the accounts of UNIMED Pharmaceuticals, Inc. (the "Company"),
and its wholly owned subsidiary, Unimed Canada, Inc.

In the opinion of the Company, the accompanying unaudited interim consolidated
financial statements contain all adjustments (consisting of normal recurring
adjustments) necessary to present fairly the Company's consolidated financial
position as of March 31, 1999, the results of operations for the three months
ended March 31, 1999 and 1998 and changes in cash flows for the three month
periods ended March 31, 1999 and 1998.

While the Company believes that the disclosures presented are adequate to make
the information not misleading, it is suggested that these condensed
consolidated financial statements be read in conjunction with the financial
statements and notes included in the Company's 1998 annual report on Form 10-K
filed with the Securities and Exchange Commission.

NOTE 2

As of January 1, 1998, the Company adopted the provisions of Statement of
Financial Accounting Standards No. 130, "Reporting Comprehensive Income." For
the three months ended March 31, 1999 and 1998, the Company had no material
comprehensive income components.


NOTE 3

In January 1999, the Company received $1,067,000 from Besins Iscovesco U.S.,
Inc. for further development in the androgen gel development programs. The
amount was recorded as deferred research and development revenue and will be
applied as research and development expenditures are incurred.


                                        7


<PAGE>   8


NOTE 4

In 1998 the Company established a provision for the remittance of higher
Medicaid rebates for Anadrol, pending a decision by the administrators of
Medicaid. In April 1999, the Company received notice from the administrators
that a lower rebate rate was appropriate. The Company reversed approximately
$700,000 (net of additional reserves) of its Medicaid rebate reserve into income
in the Fiscal 1999 Period.


NOTE 5

Certain amounts for 1998 were reclassified to conform to current year
presentation.


                                        8


<PAGE>   9

Item 2

               MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS OF
                       OPERATIONS AND FINANCIAL CONDITION


Forward-Looking Statements

When used in this discussion, the words "believes" and "expects" and similar
expressions are intended to identify forward-looking statements. Such
statements, including the Year 2000 issues discussed herein, are subject to
certain risks and uncertainties, over which the Company has no control, which
could cause actual results to differ materially from those projected. Readers
are cautioned not to place undue reliance on these forward-looking statements
that speak only as of the date hereof. The Company undertakes no obligations to
republish revised forward-looking statements to reflect events or circumstances
after the date thereof or to reflect the occurrence of unanticipated events.
Readers are also urged to carefully review and consider the various disclosures
made by the Company, in this report, as well as the Company's periodic reports
filed with the Securities and Exchange Commission.


Results of Operations

Three Months Ended March 31, 1999 vs. Three Months Ended March 31, 1998

Net sales for the three months ended March 31, 1999 (the "Fiscal 1999 Period")
increased 43% or $1,707,000 to $5,721,000 compared to net sales of $4,014,000
for the three months ended March 31, 1998 (the "Fiscal 1998 Period"). The
increase in net sales was attributable to higher unit sales in a combination of
17% sales increase in Marinol(R) (dronabinol) and 94% sales increase in
Anadrol(R) (oxymetholone), offset by a 17% decrease in Maxaquin(R) sales.
Anadrol was launched in February 1998. The Fiscal 1998 Period represents two
months sales of Anadrol, amounting to $1,450,000.

Cost of sales increased by $358,000 or 39% for the three month period ended
March 31, 1999 compared to the three month period ended March 31, 1998. This
increase is directly attributable to higher unit sales volume. Cost of sales
expressed as a percent of net sales decreased from 23% for the Fiscal 1998
Period to 22% for the same period in 1999.  This decrease is due to changes in
product mix.

Operating and administrative expenses increased in the Fiscal 1999 Period by
$349,000 or 44%. The increase is mainly attributable to a one-time severance
expense related to senior management changes. Operating and administrative
expenses as a percentage of net sales were 20% in both the Fiscal 1999 and 1998
Periods.

Sales and marketing expenses increased $372,000 to $2,456,000 in the Fiscal 1999
Period as the Company continued to expand its specialty field sales force. Sales
and marketing expenses were 43% of net sales in the Fiscal 1999 Period compared
to 52% in the Fiscal 1998 Period. The Fiscal 1998 Period amount included
approximately $1,000,000 associated with the launch of Anadrol.


                                        9


<PAGE>   10



Net research and development expenses in the Fiscal 1999 Period were $1,517,000
compared to $2,105,000 in the Fiscal 1998 Period, a decrease of 28%. Research
and development expenses were 27% of net sales for the Fiscal 1999 Period and
52% of net sales for the Fiscal 1998 Period. This planned decrease in research
and development spending is due to the completion of Phase III studies related
to Androgel(TM), the Company's testosterone replacement product, in 1998. The
decrease is also attributable to fewer clinical trials conducted during the
Fiscal 1999 Period. In addition, Fiscal 1998 Period expenses included costs
associated with the filing of the Cryptaz(TM) new drug application.

Net loss for the Fiscal 1999 Period was $328,411 or four cents per share
(basic). Net loss for the Fiscal 1998 Period was $1,706,921 or nineteen cents
per share (basic). The outstanding options for the Fiscal 1999 and 1998 Periods
were antidilutive and therefore diluted earnings per share is not presented.


Liquidity and Capital Resources

At March 31, 1999, the Company had cash, cash equivalents and short-term
investments of $8,355,000, compared to $7,487,000 at December 31, 1998, an
increase of $867,558. This increase is primarily the result of increased
receivable collections and timing of inventory shipments.

The Company used net cash in operations totaling $437,000 for the quarter ended
March 31, 1999. Current receivables decreased by $655,000 due primarily to
timely collections of receivables on fourth quarter 1998 sales. Inventories
increased $592,000 due to the timing of new inventory deliveries.

In 1998 the Company established a provision for the remittance of higher
Medicaid rebates for Anadrol, pending a decision by the administrators of
Medicaid. In April 1999, the Company received notice from the administrators
that a lower rebate rate was appropriate and therefore the Company reversed
approximately $700,000 (net of additional reserves) of its Medicaid rebate
reserve into income in the Fiscal 1999 Period.

In January 1999, the Company received $1,067,000 from Besins Iscovesco U.S.,
Inc. for further development in the androgen gel development programs. The
amount was recorded as deferred research and development revenue and will be
applied as research and development expenditures are incurred.

The Company believes that its existing cash and investment balances are adequate
to fund cash requirements for 1999 and the foreseeable future. However, certain
factors could affect the need for additional cash, such as product development,
new product launches, and sales and marketing efforts.


                                       10


<PAGE>   11


Year 2000 Program

The Year 2000 issue concerns the inability of many computer systems and other
equipment to properly recognize and process date-sensitive information during or
after the Year 2000 because their computer chips or processors use only two
digits to represent the year. As a result, business and governmental entities
are at risk for possible miscalculations or system failures causing disruptions
in their business operations. A Year 2000 problem can arise at any point in the
Company's product development, supply, manufacturing, data processing,
distribution and financial operations. The Company uses computer systems for
internal data processing, record-keeping and inventory management, and for the
compilation and evaluation of product development data.

The Company has implemented a year 2000 readiness program with the objective of
having all of its significant business systems functioning properly with respect
to Year 2000 issues well before January 1, 2000. The Company's Year 2000
readiness program is being addressed in steps, and to a large extent is being
implemented on a system-by-system or computer-by-computer basis. The first step
is the identification of the Company's critical business systems. The second
step is evaluation of the Company's critical business systems to determine the
need for remediation or replacement. The third step is the actual remediation
and replacement of material business systems, and the fourth step is testing and
implementation. The Company is currently operating in the fourth step of the
readiness program.

The Company has identified substantially all of its business systems that could
encounter Year 2000 problems. Because within the normal course of business the
Company has upgraded its systems, substantially all of the Company's business
systems and related software are Year 2000 compliant. The Company is primarily
using internal personnel and to a lesser extent contract programmers and vendors
to complete the evaluation steps of its program, to modify codes and software in
business systems that require remediation, and to test the business systems. The
Company has identified the computer hardware and software that need to be
replaced and is in the process of cost negotiations. The Company does not
believe that it will encounter difficulties or unreasonable costs in making any
hardware or software replacements necessary to substantially achieve Year 2000
readiness. The Company currently anticipates any additional costs associated
with further Year 2000 readiness will not be a material amount. Additional costs
could be incurred if the Company finds it necessary to engage outside
consultants to complete its contingency plan or if its contingency plan is
implemented. Year 2000 program costs are being funded out of cash flow and,
except for the depreciation of capital items, are being expensed as they are
incurred.

The Company relies on third party suppliers for raw materials, contract
manufacturing, transportation, product distribution, product testing and
development, and other key services ("Key Service Providers"). The Company is
currently surveying its Key Service Providers to reasonably determine their
state of Year 2000 readiness. Most of the Company's Key Service Providers are
public companies or subsidiaries of public companies or are public institutions
and utilities and, accordingly, have similar responsibilities to those of the
Company regarding Year 2000 readiness. The Company 


                                       11


<PAGE>   12



is also developing contingency plans to replace Key Service Providers that it
determines will not be Year 2000 compliant as to the Company's needs before
January 1, 2000.

The Company believes that temporary interruptions to its business could be
encountered if some or all of its Key Service Providers do not timely achieve
Year 2000 readiness. There is a risk of short-term interruption in the supply of
raw materials, manufacturing of product, processing sales, and conducting and
reporting clinical studies and other product development information. Product
sales could be deferred if communications with supply warehouses and
distributors should fail. Such disruptions and delays could result in deferred
or lost revenue and increased expenses. The Company is finalizing the
contingency plan to reduce the risk of interruptions in its business. The
contingency plan is expected to include the identification of replacement Key
Service Providers, the build-up of raw material and finished product inventories
to assure product availability, and the arrangement of alternative facilities
and equipment for testing and operations, should the need arise. The Company's
contingency plan will be designed to manage, not fully eliminate the potential
for disruptions due to Year 2000 problems.

The Company's Year 2000 readiness program is an ongoing process and the risk
assessments and estimates of costs and completion dates for various steps and
components of the program are subject to change. The cost of the Year 2000
program and the dates on which the Company believes the steps of the program
will be completed are based on management's best estimates, which were derived
using numerous assumptions of future events. Factors that could cause such
changes include, among other things, availability of qualified personnel and
consultants, the actions of third parties, primarily Key Service Providers, and
material changes in governmental regulations affecting the Company's products.
There can be no guarantee that these estimates will be achieved and actual
results could differ materially from those anticipated.


                                       12


<PAGE>   13


PART II - OTHER INFORMATION


Item 1.        Legal Proceedings                      None


Item 2.        Changes in Securities                  None


Item 3.        Defaults Upon Senior Securities        None


Item 4.        Submission of Matters to Vote          None
                of Security Holders

Item 5.        Other Information                      Reporting the change in
                                                      Chief Executive Officer
                                                      and President of the
                                                      Company

Item 6.        Exhibits and Reports on Form 8-K

                  (a) Exhibits                        27

                  (b) Reports on Form 8-K             Form 8-K filed on February
                                                      19, 1999.


                                       13


<PAGE>   14


                                 SIGNATURE PAGE


Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this Report to be signed on its behalf by the
undersigned thereunto duly authorized.



                                     UNIMED PHARMACEUTICALS, INC.






Date: May 13, 1999                   By: /s/ Robert E. Dudley
      --------------                    --------------------------------------
                                        Robert E. Dudley
                                        President and Chief Executive
                                         Officer and Director




Date: May 13, 1999                   By: /s/ David E. Riggs
      --------------                    --------------------------------------
                                        David E. Riggs
                                        Senior Vice President, Chief Financial
                                        Officer, Secretary and Treasurer



                                       14