We describe a vacuum system for the HYLIFE and Cascade inertial-confinement-fusion reactor concepts that consists of an axial-flow compressor followed by mechanical booster pumps in series having a combined total of four stages. Vacuum components are placed outside the reactors and operate at a temperature of 300 K. Pumping speeds necessary to remove hydrogen isotopes and helium from the reactors were conservatively calculated to be a maximum of 24 to 36 m3/s at 1.3 Pa (10−2 Torr) when laser drivers are used and 310–620 m3/s at 0.13 Pa (10−3 Torr) when heavy-ion-beam drivers are used. Openings in the reactors, required for illumination of the fuel pellets and for establishing the flowing blankets inside the reactors, have large enough conductances for removal of the gases from inside the reactors. A fuel recovery system separates deuterium and tritium from hydrogen and helium. The former are recycled for use in manufacturing fuel pellets.