The neutron spectra produced by the 51V(p,n)51Cr, 59Co(p,n)59Ni, 48Ti(α,n)51Cr, and 56Fe(α,n)59Ni reactions were measured at five angles between 15 and 135° for proton energies between 7.8 and 14.7 MeV, and for α energies between 11.5 and 22.7 MeV. Spectra at low energies were used to obtain the spin-weighted level density of the residual nuclei 51Cr and 59Ni. Comparison of these spectral shapes with those obtained at higher energies made possible a separation of the higher-energy spectra into compound and noncompound contributions. The deduced compound-nuclear cross sections to given groups of levels were related to the integrals of the level densities of the residual nuclei; the variation of these cross sections with energy was used to extend the level-density measurements beyond the neutron binding energy. A constant-temperature level-density form is found to be appropriate for 51Cr and 59Ni up to residual excitation energies of 14 MeV. Values of the moment of intertia of the residual nuclei were extracted from the magnitude of the asymmetry of the compound-nuclear angular distributions. The characteristics of the noncompound portion were compared with those expected from direct- and pre-equilibrium-reaction mechanisms. It is concluded that no convincing evidence for a pre-equilibrium component is observed in the (α,n) spectra; the (p,n) data show behavior consistent with contributions from both pre-equilibrium- and direct-reaction mechanisms. A value of approximately 160 keV was obtained for the widths of the participating doorway states from a model-dependent calculation based on the magnitude of the pre-equilibrium (p,n) cross section.