Prompt-fission-neutron multiplicities were measured for 238U(n,f) and 235U(n,f) from 0.4 to 200 MeV. The data are of great importance in connection with accelerator-coupled nuclear reactor systems incinerating actinides. We report that fission induced by 200 MeV neutrons produces approximately 10 more prompt neutrons than fission induced by reactor neutrons. Most neutrons are evaporated from the fission fragments and the prefission compound nucleus, as the preequilibrium emission of energetic neutrons accounts for a maximum of 15% of the prompt neutrons at 200 MeV.