Cross sections for nonresonant transfer excitation (NTE) are calculated for collisions of He-3+ with H-2 (2H) and He targets in the 50-500-keV impact-energy range. Single-electron capture probabilities to the 2s and 2p orbitals of He and single-electron excitation probabilities for He+ (1s --> 2s or 2p) transitions are independently computed, as a function of impact parameter, using the semiclassical multichannel-impact-parameter model with an expansion in atomic orbitals placed either on one or both centers. NTE cross sections for the (2s2)1S, (2p2)1D, and (2S2P)1P states, computed in the independent-electron model, are compared with the recent high-resolution electron data for transfer excitation into these states. For He+ + H-2 collisions, NTE is found to contribute primarily at the low collision energies, dropping off at the higher energies. On the contrary, for the symmetric He+ + He collisions, NTE cross sections do not drop off with impact energy as expected. In the case of the (2p2)1D state, an increase in the cross section, similar to the experimental data, is seen. However, in both cases, the calculated cross section seems to be larger than the experimental data.