The system of nonlinear evolution equations was obtained for describing the time evolution of densities of pump, signal and idler microcavity polaritons. It was shown that the period and amplitude of oscillations of the polariton densities essentially depend on the initial densities of polaritons, initial phase difference and resonance detuning. For the definite relation between the parameters it is possible the appearance of the aperiodic evolution of the system, which represents the conversion only the part of pump polaritons, by which the evolution of the system is finished. The significant dependence of the period and amplitude of polariton oscillations on the initial phase difference evidences about the possibility of the phase controlling of the polariton dynamics. The damping of the system of coherent polaritons leads to the oscillatory decay of polariton density in time, the rate of which is defined by the polariton damping constants.