The energy distribution of neutrons from proton-nucleus nonelastic collisions for 18-MeV protons on 14N, 27Al, 56Fe, 181Ta, and 208Pb and for 15-MeV protons on 27Al and 208Pb have been calculated with the intranuclear-cascade-evaporation model of nuclear reactions and with the evaporation model of nuclear reactions. Comparisons between the calculated neutron spectra and experimental data are presented, and it is shown that neither model is entirely reliable in the energy region considered but that the intranuclear-cascade-evaporation model is the more reliable of the two.