In microwave sources of coherent Čerenkov radiation the electrons usually propagate near the rippled wall of a slow-wave structure. These ripples cause the periodic modulation of electron potential depression, and therefore, lead to periodic modulation of electron axial velocities. Since the period of this electrostatic pumping is the period of the slow-wave structure the parametric coupling of electrons to originally nonsynchronous spatial harmonics of the microwave field may occur. This effect can be especially important for backward-wave oscillators (BWO’s) driven by high current, relativistic electron beams. In the paper both linear and nonlinear theories of the relativistic resonant BWO with periodic modulation of electron axial velocities are developed and results illustrating the evolution of the linear gain function and the efficiency of operation in the large-signal regime are presented.