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The multistep compound formalism of Feshbach, Kerman, and Koonin has been extended to include y-ray emission. By allowing the first few simple preequilibrium bound states to decay via electromagnetic transitions rather than particle emission, the large number of high-energy y rays observed in the experimental data can be understood. It is assumed that single-particle and -hole transitions lead to the emission of y rays, and radial matrix elements for such transitions are estimated by exploiting the inverse process, photoabsorption.Reactions of 14-MeV neutrons with ' Co, 'Nb, and "'Ta are analyzed and it is found that between 20% and 50% of cross sections for high-energy y-ray emission can be accounted for by the multistep compound mechanism. 421652