It is shown that the saw-tooth variation of the cavity length in a photorefractive semilinear coherent oscillator can suppress the instability in the frequency domain and prevent a bifurcation in the oscillation spectrum. To achieve such a suppression the frequency of the cavity length modulation should be chosen appropriately. It depends on the photorefractive crystal parameters (electrooptic properties, photoconductivity, dimensions) and on the experimental conditions (pump intensity ratio, orientation of the pump and oscillation waves with respect to the crystallographic axes, polarization of the pump waves, etc. ). It depends also strongly on a possible misalignment of the two pump waves. On the other hand, within a certain range of the experimental parameters the mirror vibration may lead to a further frequency splitting in the already existing two-mode oscillation spectrum.