The spontaneous and induced emission from a free-electron laser is treated for the case in which an axial magnetic field is imposed in addition to the helical, axially periodic wiggler magnetic field. The classes of possible single-particle trajectories in this configuration are discussed, and the results are applied to a calculation of the incoherent radiation from a beam of relativistic electrons in the system. The coherent radiation is treated by solving the Vlasov-Maxwell equations for the linear gain in the tenuous-beam limit, where the beam plasma frequency is much less than the radiation frequency and self-field effects can be ignored.