<PAGE>   1
                                                                    EXHIBIT 11.1


                  ARONEX PHARMACEUTICALS, INC. AND SUBSIDIARIES


              Statement Regarding Computation of Per Share Earnings

The following reflects the information used in calculating the number of shares
in the computation of net loss per share for each of the periods set forth in
the Consolidated Statements of Operations.


<TABLE>
<CAPTION>
                                                                                     AVERAGE                      LOSS
                                               DAYS            SHARES                SHARES                        PER
                               SHARES       OUTSTANDING        X DAYS              OUTSTANDING        LOSS        SHARE
<S>                            <C>          <C>            <C>                     <C>            <C>             <C>
Year Ended December 31, 1998:  15,459,166        11          170,050,826
                               15,460,684        71        1,097,708,564
                               15,465,729         1           15,465,729
                               15,467,281        97        1,500,326,257
                               15,497,443        92        1,425,764,756
                               15,503,745         1           15,503,745
                               15,503,745        40          620,149,800
                               15,508,745         9          139,578,705
                               15,509,301         5           77,546,505
                               16,347,290        23          375,987,670
                               16,349,706         6           98,098,236
                               16,352,277         6           98,113,662
                               16,352,763         2           32,705,526
                               16,379,309         1           16,379,309
                                                365        5,683,379,290  /365      15,570,902    (18,231,000)    (1.17)
</TABLE>


                                   Page 1 of 4
<PAGE>   2
<TABLE>
<CAPTION>
                                                                                     AVERAGE                      LOSS
                                               DAYS            SHARES                SHARES                        PER
                               SHARES       OUTSTANDING        X DAYS              OUTSTANDING        LOSS        SHARE
<S>                            <C>          <C>            <C>                     <C>            <C>             <C>
Year Ended December 31, 1997:  14,597,247        8            116,777,976
                               14,606,972       12            175,283,664
                               14,612,023        4             58,448,092
                               14,612,499       21            306,862,479
                               14,615,983        6             87,695,898
                               14,616,981        1             14,616,981
                               14,624,239        5             73,121,195
                               14,625,111        2             29,250,222
                               14,627,695        7            102,393,865
                               14,628,567        6             87,771,402
                               14,640,311        6             87,841,866
                               14,643,658        6             87,861,948
                               14,644,672        1             14,644,672
                               14,644,816        7            102,513,712
                               14,644,982        2             29,289,964
                               14,645,277        4             58,581,108
                               14,665,277       22            322,636,094
                               14,665,665        9            131,990,985
                               14,674,453       19            278,814,607
                               14,678,042        6             88,068,252
                               14,680,055        7            102,760,385
                               14,680,344       19            278,926,536
                               14,687,394       31            455,309,214
                               14,710,122        9            132,391,098
                               14,712,069        5             73,560,345
                               14,712,575       12            176,550,900
                               14,712,699        6             88,276,194
                               14,714,018        2             29,428,036
                               14,719,923        9            132,479,307
                               15,406,372       15            231,095,580
                               15,408,872        3             46,226,616
                               15,421,809        9            138,796,281
                               15,423,809        2             30,847,618
                               15,427,540       24            370,260,960
                               15,444,824       57            880,354,968
                               15,459,166        1             15,459,166
                                               365          5,437,188,186  /365      14,896,406   (16,991,000)    (1.14)
</TABLE>


                                   Page 2 of 4

<PAGE>   3
<TABLE>
<CAPTION>
                                                                                     AVERAGE                      LOSS
                                               DAYS            SHARES                SHARES                        PER
                               SHARES       OUTSTANDING        X DAYS              OUTSTANDING        LOSS        SHARE
<S>                            <C>          <C>            <C>                     <C>            <C>             <C>
Year Ended December 31, 1996:  10,380,056        1            10,380,056
                               10,390,003       10           103,900,030
                               10,409,608        4            41,638,432
                               10,418,676        2            20,837,352
                               10,478,786        1            10,478,786
                               10,046,458        3            30,139,374
                               10,598,792        1            10,598,792
                               10,678,561        2            21,357,122
                               10,680,653        1            10,680,653
                               10,680,903        3            32,042,709
                               10,710,132        4            42,840,528
                               10,718,504        6            64,311,024
                               10,727,170        4            42,908,680
                               10,728,565        1            10,728,565
                               10,729,263        1            10,729,263
                               10,729,394        7            75,105,758
                               10,731,487       19           203,898,253
                               10,742,559        7            75,197,913
                               10,771,115        2            21,542,230
                               10,775,477        2            21,550,954
                               10,776,991        4            43,107,964
                               10,784,842        1            10,784,842
                               10,812,921        1            10,812,921
                               10,832,546        2            21,665,092
                               10,847,725        3            32,543,175
                               10,848,023        5            54,240,115
                               10,849,767        7            75,948,369
                               10,851,626        3            32,554,878
                               10,858,605        1            10,858,605
                               10,862,095        2            21,724,190
                               10,962,004        1            10,962,004
                               10,962,593        4            43,850,372
                               10,965,241        2            21,930,482
                               10,965,939        1            10,965,939
                               10,967,993        6            65,807,958
                               10,927,354        5            54,636,770
                               10,997,354        2            21,994,708
                               10,978,310        7            76,848,170
                               10,983,980        4            43,935,920
                               10,989,215        1            10,989,215
                               13,992,587        1            13,992,587
                               13,996,077        1            13,996,077
                               13,996,949        6            83,981,694
                               14,446,949        1            14,446,949
                               14,453,492        5            72,267,460
                               14,456,109        5            72,280,545
                               14,465,806        1            14,465,806
                               14,472,786        2            28,945,572
                               14,473,658        1            14,473,658
                               14,478,658        3            43,435,974
                               14,481,500        1            14,481,500
                               14,483,680        3            43,451,040
                               14,484,059        1            14,484,059
                               14,485,899        2            28,971,798
                               14,488,079        3            43,464,237
                               14,526,802       26           377,696,852
                               14,531,016        1            14,531,016
                               14,543,516       20           290,870,320
                               14,543,736        1            14,543,736
                               14,544,318       18           261,797,724
                               14,545,238        2            29,090,476
                               14,545,321        7           101,817,247
                               14,555,018       14           203,770,252
                               14,556,217        5            72,781,085
                               14,557,089        8           116,456,712
                               14,563,193       17           247,574,281
                               14,568,375        3            43,705,125
                               14,569,375        7           101,985,625
                               14,570,954        3            43,712,862
                               14,579,548        4            58,318,192
                               14,582,198        1            14,582,198
                               14,583,853        3            43,751,559
                               14,584,853        3            43,754,559
                               14,586,353       14           204,208,942
                               14,595,950       10           145,959,500
                               14,596,513       11           160,561,643
                               14,597,247        8           116,777,976
                                               365         4,762,415,001  /365      13,047,712    (8,030,000)     (0.62)
                                               
</TABLE>


                                   Page 3 of 4

<PAGE>   4
<TABLE>
<CAPTION>
                                                                                     AVERAGE                      LOSS
                                               DAYS            SHARES                SHARES                        PER
                               SHARES       OUTSTANDING        X DAYS              OUTSTANDING        LOSS        SHARE
<S>                            <C>          <C>            <C>                     <C>            <C>             <C>
Year Ended December 31, 1995:
                                5,202,476        2           10,404,952
                                5,214,976        2            10,429,952
                                5,221,604       82           428,171,528
                                5,232,463       57           298,250,391
                                5,233,599       41           214,577,559
                                5,233,978       18            94,211,604
                                5,235,493       51           267,010,143
                                9,128,929       20           182,578,580
                                9,136,184       34           310,630,256
                                9,200,154        3            27,600,462
                                9,201,669        2            18,403,338
                                9,202,805       12           110,433,660
                                9,216,760        1             9,216,760
                                9,217,843        6            55,307,058
                                9,260,401        3            27,781,203
                                9,274,343        5            46,371,715
                                9,316,912        2            18,633,824
                                9,857,533        5            49,287,665
                                9,887,531        5            49,437,655
                                9,899,311        2            19,798,622
                                9,900,249        2            19,800,498
                                9,902,749        4            39,610,996
                                9,969,021        2            19,938,042
                                9,981,786        3            29,945,358
                               10,380,056        1            10,380,056
                                               365         2,368,211,877   /365       6,488,252   (17,429,000)     (2.69)
</TABLE>


                                   Page 4 of 4