The counter-propagation artificial neural network (CP ANN) technique was applied for the independent variable selection and for structure-mutagenic potency modeling on a set of 95 aromatic and heteroaromatic amines with biological activity investigated experimentally by an in vitro assay. The molecular structures were represented by 275 independent variables classified as topostructural, topochemical, geometrical and quantum-chemical descriptors. As a result of the neural network modeling, the following descriptors were found to be the most important for structure-activity relationship: (5)chi-path connectivity index of order h = 5, (3)chi(b) (C)-bond cluster connectivity index of order h = 3, J(B)-Balaban's J index based on bond types, SHSNH2-electrotopological state index values for atoms, phia-flexibility index (kappa p1x kappa p2/nvx), IC0-mean information content or complexity of a graph based on the 0 order neighborhood of vertices in a hydrogen-filled graph and E-LUMO. The leave one out (LOO) method was used in order to test and select the models for mutagenicity prediction. The statistical parameters for the 7-descriptors model are R-Model = 0.96 and R-cv = 0.85, respectively. In the next step, the number of variables was reduced and the 4-descriptors model was found (R-Model = 0.95 and R-cv = 0.85) and classified as the best one.