The dynamics of optical parametric exciton-polariton oscillations in semiconductor microcavities was studied, taking into account the conversion processes of the two pump polaritons into signal and idler polaritons and vice versa. The system of nonlinear evolution equations was obtained for describing the time evolution for the densities of pump, signal and idler polaritons. The periodic and aperiodic regimes of the evolution of polariton densities exist. 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, the aperiodic evolution of the system is possible, too, representing the conversion of only part of the pump polaritons, which finishes the evolution of the system. The significant dependence of the period and amplitude of polariton oscillations on the initial phase difference is evidence of 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.