The differential cross sections for the production of gamma radiation from fast-neutron inelastic scattering have been measured at incident neutron energies from 4.00 to 7.67 MeV for Be, C, O, Al, Si, Fe, Ni, Nb, W, and 239Pu. The gamma-ray spectra were measured with a NaI(Tl) spectrometer using time-of-flight techniques to eliminate the neutron background. The gamma-ray detector was surrounded with a large NaI(Tl) annulus operated in the anticoincidence mode. The resulting spectra were unfolded and appropriate corrections were applied for neutron and gamma-ray attenuation, for electronic dead time, and for detector efficiency.