We measured neutron time-of-flight spectra from 90 MeV protons and 140 MeV alpha particles bombarding thin targets of Al, Ni, Zr, and Bi at laboratory angles between 20\ifmmode^\circ\else\textdegree\fi{} and 135\ifmmode^\circ\else\textdegree\fi{}. The lowenergy (5 to 45 MeV) portions of the spectra were measured with 5 cm diameter by 5 cm deep NE-213 counters at 1 m flight paths with n-$\ensuremath{\gamma}$ pulse-shape discrimination. The high-energy (35 to 150 MeV) portions of the spectra were measured with 12.7 cm diameter by 10.2 cm deep NE-102 counters at flight paths of 2.0 to 5.0 m. The proton-induced measured neutron spectra reveal three distinct energy regions: a low-energy evaporation region, a high-energy region dominated by the quasifree scattering process, and an intermediate-energy region dominated by multistep, preequilibrium processes. In the latter two regions, the spectra show strong angular dependence. The alpha-particle induced neutron spectra show these same distinct energy regions plus an exponential falloff above the beam energy per nucleon. The neutron spectra are compared with earlier proton spectra produced also by 90 MeV protons and 140 MeV alpha particles. It is observed that the high-energy portions of the forward-angle neutron and proton cross sections are in ratios consistent with the idea that single nucleon-nucleon scattering dominates. For the heavy-mass targets, the low-energy evaporation regions show neutron yields larger than proton yields. The proton-to-neutron ratios observed in the high-energy continua are interpreted with a quasifree calculation fitted simultaneously to the proton and the neutron spectra. Preequilibrium calculations with the exciton model and the hybrid model reproduce the shape of the experimental angle-integrated energy spectra down to lower energies than the quasifree calculations. The exciton model calculations underestimate the magnitudes of the cross sections, while the hybrid model provides better absolute agreement. One of the preequilibrium calculations uses the method of Mantzouranis and Weidenm\"uller to predict angular distributions; we find that the predicted angular distributions overestimate the neutron yields at forward angles. The intranuclear-cascade model predicts proton-to-neutron ratios much smaller than experimentally observed in the high-energy forward-angle continua.NUCLEAR REACTIONS $^{27}\mathrm{Al}$, $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, $^{209}\mathrm{Bi}$(p,n), ($\ensuremath{\alpha}$, n), ${E}_{\mathrm{p}}=90$ MeV; ${E}_{\ensuremath{\alpha}}=140$ MeV; ${\ensuremath{\theta}}_{L}=20\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}135\ifmmode^\circ\else\textdegree\fi{}$; measured $\frac{{d}^{2}\ensuremath{\sigma}}{d\ensuremath{\Omega}\mathrm{dE}}$; compared with available experimental proton spectra and with theoretical calculations including PWIA quasifree scattering, preequilibrium exciton, geometry-dependent hybrid, and intranuclear-cascade models.