<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 September 30, 1998  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                                  8,984,565
      ($.25 par value)

<PAGE>   2

                  UNIMED PHARMACEUTICALS, INC. AND SUBSIDIARY

<TABLE>
<CAPTION>
                                                                           Page 
                                                                          Number
                                                                          ------
PART I.   Financial Information
<S>               <C>                                                     <C>
       ITEM 1.    Financial Statements

                  Condensed Consolidated Balance Sheets                      3

                  Condensed Consolidated Statements of Operations            5

                  Condensed Consolidated Statements of Cash Flows            6

                  Notes to Condensed Consolidated Financial Statements       7

       ITEM 2.    Management's Discussion and Analysis of Results of         

                  Operations and Financial Condition                         8

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
CONDENSED CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                 September 30,     December 31,
                                                     1998             1997
                                                ---------------    ------------
ASSETS                                            (unaudited)        
------
<S>                                               <C>               <C>
Current assets:
Cash and cash equivalents                         $   381,859       $ 1,068,279
Short-term investments                              7,723,002        13,718,834
Receivables:
  Trade                                             2,601,057         1,661,042
  Other                                               162,760           116,978
                                                  -----------       -----------
  Total receivables                                 2,763,817         1,778,020

Inventories                                         4,598,828         4,386,904
Prepaid expenses                                      197,105           407,698
                                                  -----------       -----------
  Total current assets                             15,664,611        21,359,735

Equipment and leasehold improvements, at cost       3,007,055         2,555,857
Less accumulated depreciation and amortization      1,680,448         1,452,217
                                                  -----------       -----------

  Net                                               1,326,607         1,103,640

Product rights, net of amortization                 1,529,352         1,626,349
                                                  -----------       -----------
  Total assets                                    $18,520,570       $24,089,724
                                                  ===========       ===========
</TABLE>

    See accompanying notes to condensed consolidated financial statements.


                                       3
<PAGE>   4

ITEM 1 - FINANCIAL STATEMENTS

UNIMED PHARMACEUTICALS, INC. AND SUBSIDIARY
CONDENSED CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                        September 30,     December 31,
                                                                            1998             1997
                                                                        -------------     ------------
                                                                         (unaudited)        
<S>                                                                       <C>              <C>
LIABILITIES AND STOCKHOLDERS' EQUITY
------------------------------------
Current liabilities:
  Accounts payable                                                        $4,340,003       $ 1,812,030
  Accrued and other liabilities                                            2,530,756         1,806,687
  Due to Roxane Laboratories, Inc.                                         3,409,137         3,616,665
  Current portion of long-term obligation                                    120,000           914,836
                                                                        -------------     ------------
     Total current liabilities                                            10,399,896         8,150,218

Long-term obligation                                                         519,251         1,213,000
                                                                        -------------     ------------
     Total liabilities                                                    10,919,147         9,363,218

Stockholders' equity:
  Common stock, $.25 par value; authorized 30,000,000
  shares; issued and outstanding: 9,086,612
  and 9,040,942, respectively                                              2,271,654         2,260,236
Additional paid-in capital                                                28,385,250        28,201,420
Accumulated deficit                                                      (22,568,212)      (15,215,214)
Accumulated other comprehensive income (Note 2)                               42,731            41,522
                                                                        -------------     ------------
                                                                           8,131,423        15,287,964
Less:  treasury stock at cost (102,047 and 108,500 shares at
  respective dates)                                                         (530,000)         (561,458)
                                                                        -------------     ------------
     Total stockholders' equity                                            7,601,423        14,726,506
                                                                        -------------     ------------
Total liabilities and stockholders' equity                               $18,520,570       $24,089,724
                                                                         ============     ============
</TABLE>

    See accompanying notes to condensed consolidated financial statements.


                                        
                                       4
<PAGE>   5

UNIMED PHARMACEUTICALS, INC. AND SUBSIDIARY
CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS
THREE AND NINE MONTHS ENDED SEPTEMBER 30, 1998 AND 1997

<TABLE>
<CAPTION>
                                                    Three Months Ended                          Nine Months Ended
                                                       September 30,                              September 30,
                                                ---------------------------           ---------------------------------
                                                   1998             1997                 1998                  1997
                                                ----------       ----------           -----------            ----------
                                                                          (unaudited)
<S>                                            <C>               <C>                  <C>                    <C> 
Net sales                                      $ 4,120,833       $2,864,203           $11,542,800            $6,657,026
Cost of sales                                    1,039,827        1,045,803             2,810,124             2,264,315
                                                ----------       ----------           -----------            ----------
Gross profit                                     3,081,006        1,818,400             8,732,676             4,392,711

Operating and administrative expenses            1,143,363          561,826             2,600,314             1,825,552
Sales and marketing expenses                     1,561,987          886,445             5,729,673             1,923,857
Research and development expenses, net           3,402,019          549,327             8,071,972             1,147,966
                                                ----------       ----------           -----------            ----------
Total expenses                                   6,107,369        1,997,598            16,401,959             4,897,375
                                                ----------       ----------           -----------            ----------

Loss from operations                            (3,026,363)       (179,198)            (7,669,283)             (504,664)

Other income:
  Interest income, net                             107,347          225,112               316,285               718,419
  Product right sublicense gain                        - -          150,000                   - -               300,000
                                                ----------       ----------           -----------            ----------
(Loss) income before income taxes               (2,919,016)         195,914            (7,352,998)              513,755
Income tax expense                                     - -              - -                   - -                   - -
                                                ----------       ----------           -----------            ----------
Net (loss) income                              $(2,919,016)      $  195,914           $(7,352,998)           $  513,755
                                                ==========       ==========           ===========            ==========
Net (loss) income per share:
  Basic                                        $      (.33)      $      .02           $      (.82)           $      .06
                                                ==========       ==========           ===========            ==========
  Diluted                                                        $      .02                                  $      .06
                                                                 ==========                                  ==========
Weighted average number of common and
common equivalent shares outstanding:                             
  Basic                                          8,951,448        8,882,573             8,950,915             8,879,161
                                                ==========       ==========           ===========            ==========
  Diluted                                                         9,374,925                                   9,189,348
                                                                 ==========                                  ==========
</TABLE>

     See accompanying notes to condensed consolidated financial statements.

                                        
                                       5
<PAGE>   6

UNIMED PHARMACEUTICALS, INC. AND SUBSIDIARY
CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
NINE MONTHS ENDED SEPTEMBER 30, 1998 AND 1997

<TABLE>
<CAPTION>

                                                                          Nine Months Ended
                                                                            September 30,
                                                                  --------------------------------
                                                                      1998                1997
                                                                  -----------          -----------
                                                                             (unaudited)
<S>                                                               <C>                 <C>
Cash flows (used in) provided by operations:
Net (loss) income                                                $(7,352,998)         $   513,755
Adjustments to reconcile net (loss) income to net cash
(used in) provided by operations:
  Depreciation and amortization                                      325,228              335,466
  Other                                                                1,209                  - -
(Increase) decrease in current receivables                          (985,797)             245,015
(Increase) decrease in inventories                                  (211,924)             440,530
Decrease (increase) in prepaid expenses                              210,593             (154,220)
Increase in payables, accrued and other liabilities                3,252,042               52,431
Decrease in due to Roxane Laboratories, Inc.                        (207,528)            (928,297)
                                                                 -----------          -----------
     Net cash (used in) provided by operating activities          (4,969,175)             504,680
Cash flows used in (provided by) investing activities:
  Capital expenditures                                              (451,198)            (463,558)
  Sale of short-term investments, net                              5,995,832            2,288,448
  Product rights acquisition                                             - -           (3,376,000)
                                                                 -----------          -----------
  Net cash provided by (used in) investing activities              5,544,634           (1,551,110)
Cash flows used in financing activities:
  Issuance (purchase) of common stock from Treasury                   50,011             (561,458)
  Repayment of long-term debt                                     (1,488,585)                 - -
  Proceeds from issuance of common stock                             176,695              532,065
  Deferred research and development revenues, net                        - -           (1,232,742)
                                                                 -----------          -----------
     Net cash used in financing activities                        (1,261,879)          (1,262,135)
                                                                 -----------          -----------

Decrease in cash and cash equivalents                               (686,420)          (2,308,565)
Cash and cash equivalents at beginning of period                   1,068,279            4,458,889
                                                                 -----------          -----------
Cash and cash equivalents at end of period                       $   381,859          $ 2,150,324
                                                                 ===========          ===========
Supplemental disclosures of cash flow information:
Cash paid during the period for:
  Income taxes                                                          $ --                 $ --
Obligation assumed due to product rights acquisition,
including imputed interest                                              $ --          $ 1,697,000
</TABLE>

     See accompanying notes to condensed consolidated financial statements.


                                        
                                       6
<PAGE>   7


                  UNIMED PHARMACEUTICALS, INC. AND SUBSIDIARY
              Notes to Condensed Consolidated Financial Statements
                               September 30, 1998
                                  (Unaudited)


NOTE 1

The condensed consolidated financial information herein is unaudited, other
than the Condensed Consolidated Balance Sheet at December 31, 1997, 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 September 30, 1998, the results of operations for the three and
nine months ended September 30, 1998 and 1997 and changes in cash flows for the
nine month periods ended September 30, 1998 and 1997.

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 1997 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."
Total comprehensive income, related wholly to currency translation adjustments,
for the nine months ended September 30, 1998 and 1997 were $1,209 and ($56),
respectively, and $823 and ($143) for the three months ended September 30, 1998
and 1997, respectively.


NOTE 3

Certain amounts for 1997 were reclassified to conform to current year
presentation. 


                                       7
<PAGE>   8

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
which 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

Nine Months Ended September 30, 1998 vs. Nine Months Ended September 30, 1997

Net loss for the nine months ended September 30, 1998 (the "Fiscal 1998 Period")
was $7,352,998 or eighty-two cents per share (basic). The outstanding options
for the Fiscal 1998 Period were antidilutive and therefore not presented on a
per share basis.  Net income for the nine months ended September 30, 1997 (the
"Fiscal 1997 Period") was $513,755 or six cents per share (basic and diluted).

Net sales for the Fiscal 1998 Period increased by 73% or $4,885,774 to
$11,542,800 compared to net sales of $6,657,026 for the Fiscal 1997 Period. The
increase in net sales was due to higher unit volume of Marinol(R) (dronabinol)
and Maxaquin(R) (lomefloxacin), resulting in a 28% increase in both products'
sales. In addition, Anadrol(R) (oxymetholone), an oral anabolic androgen,
generated net sales of $2,999,506.   Anadrol(R) was launched in April, 1998.

Cost of sales increased by $545,809 or 24% for the Fiscal 1998 Period compared
to the Fiscal 1997 Period due primarily to higher unit volume.  Cost of sales
expressed as a percent of net sales decreased to 24% for the nine month period
ended September 30, 1998 from 34% for the same period in 1997, due primarily to
product mix.

Operating and administrative expenses for the nine months ended September 30,
1998 increased by $774,762 or 42% primarily due to increases consulting and
outsourcing services.  Operating and administrative expenses as a percentage of
net sales were 23% and 27% for Fiscal 1998 and 1997 Periods, respectively.


                                       8
<PAGE>   9

Sales and marketing expenses increased $3,805,816 to $5,729,673 in the Fiscal
1998 Period with the growth in the sales force that in turn increased product
sales. The sales and marketing spending increase was also attributable to the
continuation of the Company's product promotion in targeted physician specialty
markets and costs related to the launch of Anadrol(R).  Sales and marketing
expenses were 50% of net sales in the Fiscal 1998 Period compared to 29% in the
Fiscal 1997 Period.

Research and development expenses in the Fiscal 1998 Period were $8,071,972 (net
of research and development revenues of $203,791), compared to $1,147,966 (net
of research and development revenues of $1,272,911) in the Fiscal 1997 Period.
Net research and development expenses were 70% of net sales for the Fiscal 1998
Period and 17% of net sales for the Fiscal 1997 Period.  Research and
development spending increased with the acceleration of Phase III studies
related to Androgel(TM), the Company's topical testosterone replacement gel,
expenses associated with the nitazoxanide NDA filing, the addition of clinical
and regulatory staff to manage clinical development programs and Phase III
studies related to the development of Andractim(TM), a topical gel used to treat
androgen deficiency in older males.  Andractim(TM) contains dihydrotestosterone
(DHT), a natural male hormone.

The Company expects the current level of research and development expenses,
which are partially offset by research and development revenues, to continue as
planned product development continues through the end of 1998, but to decline in
1999.


Three Months Ended September 30, 1998 vs. Three Months Ended September 30, 1997

Net loss was $2,919,016 or thirty-three cents per share (basic) for the three
months ended September 30, 1998. The options outstanding were antidilutive and
therefore not presented on a per share basis.  Net income for the three months
ended September 30, 1997 was $195,914 or two cents per share (basic and
diluted).

Net sales for the three months ended September 30, 1998 were $4,120,833,
representing an increase of 44% or $1,256,630 compared to net sales of
$2,864,203 for the three months ended September 30, 1997.  The increase in net
sales was attributable to increased sales volume from Marinol(R) and Maxaquin(R)
and sales of $877,999 from Anadrol(R) launched in 1998.

Cost of sales decreased by $5,976 or 1% for the three month period ended
September 30, 1998 compared to the three month period ended September 30, 1997.
This decrease is due to raw material rework expenses incurred in 1997 and to
changes in product mix. Cost of sales expressed as a percent of net sales
decreased to 25% from 37% for the same period in 1997.

Operating and administrative expenses increased during the three month period
ended September 30, 1998 by $581,537 or 104%.  Operating and administrative
expenses as a percentage of net sales were 28% in the three months ended
September 30, 1998 


                                       9



<PAGE>   10


compared to 20% for the same period in 1997.  The increase was attributable to
consulting and outsourcing services.

Sales and marketing expenses increased $675,542 or 76% in the three month period
ended September 30, 1998 and related to the expanded sales force and management.
Sales and marketing expenses were 38% and 31% of net sales in the three month
period ended September 30, 1998 and 1997, respectively.

Net research and development expenses, net of revenues of $128,171, were
$3,402,190 for the three month period ended September 30, 1998.  For the same
period in 1997, net research and development expenses were $549,327, offset by
$527,851 of revenue.  Net research and development expenses represented 83% and
19% of net sales for the three month periods ended September 30, 1998 and 1997,
respectively.  The increase is due to the addition of clinical and regulatory
staff to manage clinical development programs and clinical study expenses.

Liquidity

At September 30, 1998, the Company had cash, cash equivalents and short-term
investments of $8,104,861 compared to $14,787,113 at December 31, 1997, a
decrease of $6,682,252.

The Company used net cash for operations totaling $4,969,175 for the nine months
ended September 30, 1998.  The Company's use of cash was primarily used to fund
the net loss of $7,352,998 for that period.  The net loss was principally due to
research and development spending amounting to $8,071,972. Current receivables
increased by $985,797 due to the increase in sales across all product lines.
Inventories increased $211,924 due to the ongoing product sales and the timing
of new inventory deliveries.   Payables, accrued and other liabilities increased
$3,252,042 due primarily to the reduction in gross sales for anticipated
product-related rebates, chargebacks, returns and discounts.

The Company believes that its existing cash and investment balances are adequate
to fund cash requirements for 1998 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.

Year 2000 Issues

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 an 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.

                                        
                                       10



<PAGE>   11


The Company is in the process of implementing a year 2000 readiness program with
the objective of having all of its significant business systems functioning
properly with respect to year 2000 issues 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 material business systems.
The second step is evaluation of the Company's material 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 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 ready.  The Company is using
primarily 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 anticipates that some of its computer hardware and
software will need to be replaced.  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
in the process of 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 similarly responsibilities to
those of the Company regarding Year 2000 readiness.   The Company is also
developing contingency plans to replace Key Service Providers that it determines
will not be Year 2000 ready 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 in the process of
developing a 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


                                       11
<PAGE>   12


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
component 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

<TABLE>
<CAPTION>

<S>              <C>                                                  <C>
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                                    None

Item 6.          Exhibits and Reports on Form 8-K

                 (a)  Exhibits
                 (b)  Reports on Form 8-K                             None
</TABLE>


                                       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: November 16, 1998                By: /s/  Ronald L. Goode
      -----------------                   -------------------------------------
                                          Ronald L. Goode
                                          President and Chief Executive Officer



Date: November 16, 1998                By: /s/ David E. Riggs
      -----------------                   -------------------------------------
                                          David E. Riggs
                                          Senior Vice President, Chief Financial
                                                Officer, Secretary and Treasurer


                                       14