Stimulated microwave emission from E\ifmmode\times\else\texttimes\fi{}B drifting electrons in slow-wave cavities occurs when the Doppler-shifted radiation frequency is either near zero or the electron cyclotron frequency. The former case, characterized by the synchronous drift velocity u, \ensuremath{\omega}-ku\ensuremath{\simeq}0, corresponds to the ``pure drift'' instability, while the latter, satisfying \ensuremath{\omega}-ku\ensuremath{\simeq}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}, is termed the ``drift-cyclotron'' mode. In both cases the drift kinetic energy and momentum are invariant during radiative transitions. The momentum of the emitted or absorbed radiation quantum comes from the vector potential associated with the static magnetic field and induces a shift of the electron guiding center in a direction transverse to the drift velocity. In the pure drift case the radiation energy comes from the change in the electrostatic potential energy. In the drift-cyclotron case both electrostatic and cyclotron rotation energies are converted into radiation. In the nonrelativistic regime the gain is symmetric with respect to the frequency detuning from resonance. The difference between the stimulated absorption and emission probabilities, responsible for the gain, is caused by field gradients across the direction of the electron drift. These gradients come from the waveguide mode structure and the collective field of the electron beam. The drift mode is always unstable, while there exists one stable and one unstable drift-cyclotron branch. Relativistic mass effects influence only the drift-cyclotron instability, adding a gain contribution that is antisymmetric in frequency detuning.