The synthesis of 2,3,5-substituted perhydropyrrolo[3,4-d]isoxazole-4,6-diones (44 compounds) has been accomplished by the cycloaddition reaction of N-methyl-C-arylnitrones with N-substituted maleimides. The compounds were screened for their antibacterial activities and most of them exhibited activity against Enterococcus faecalis (ATCC 29212) and Staphylococcus aureus (ATCC 25923). cis-3a and cis-3d were found fairly effective against E. faecalis (ATCC 29212) and S. aureus (ATCC 25923) with MIC values of 25 and 50 μg/ml. With the changes of cis isomers of the compounds to trans, their antibacterial activities also changed against the bacteria studied. First, pharmacophoric fragments had been calculated in accordance with the rules of the electronic-topological method (ETM). Next, both active compounds and pharmacophores had been projected to the nodes of Kohonen's self-organizing maps (SOM) to obtain the weights of pharmacophore fragments as numerical descriptors, that were used after this for the associative neural networks (ASNN) training. A model for the activity prediction was developed as the result of training the ASNNs.