The results obtained by measuring cross sections for the formation of fragments originating from 241Am and 237Np fission induced by 660-MeV protons are presented. The charge and mass distributions of fragments are analyzed within the multimode-fission model, symmetric and asymmetric fission channels being separated. The contributions of various fission components are estimated, and the fission cross sections for the 241Am and 237Np nuclei are calculated along with the fissilities of these nuclei.