The theory of grating oscillations in photorefractive materials is developed in the linear and nonlinear approximations for the drift mechanism of holographic recording. The resonance dependence of diffraction efficiency on the phase-modulation frequency is predicted for the linear regime in which holograms are recorded by two beams, one of which is phase modulated. For long drift lengths (K g L 0 1) the resonance frequency is shown to be r ( 1 K g L 0 ) 1 . A more pronounced resonance peak is expected for the non-Bragg diffraction orders. In the nonlinear regime of recording, additional resonance maxima at r /p ( p is an integer) are found. Grating oscillations are experimentally studied in thin holograms of Bi 12 TiO 20 . A sharp resonance for the non-Bragg order in the interval 100 2000 Hz is detected. The position of the resonance is shown to depend on the experimental conditions. The experiment is in excellent agreement with the theory. At a high contrast ratio and in a high external electric field, distortions in the resonance dependence at r and even a chaotic frequency dependence are found, which points to the nonlinear character of grating oscillations. 1998 Optical Society of America S0740-3224(98)03707-2