Abstract We investigate the bistable and multistable response of the phase conjugate reflectivity (PCR) for the case of a linear photorefractive (PR) oscillator in presence of the moving grating operation. Numerical evaluation of stable multiple solutions of the PCR shows enhancement, bistable, multistable and self-oscillating behaviours with respect to the control parameters like the frequency-shift (Ω) due to grating motion, reflectivities (M 1 and M 2) of cavity mirrors, the coupling strength (of complex gL and real g 0 L values) and the PR phase shift (φPR). If the different branches are assumed to be stable, multistable but isolated branching behaviour with an increased PCR can be predicted. Results are interpreted physically by considering the competitions between (i) the strengths of two moving transmission gratings that arise from A1–A4 (forward oscillating pump-incident) and A2–A3 (backward oscillating pump-phase conjugate) interferences and (ii) the applied frequency detuning that causes the gra...