Semiconductor microcavities with embedded quantum wells exhibit rich variety of unusual light-matter coupling effects. In the regime of strong coupling the excitons and photons are mixed into a kind of quasiparticles, known as the cavity exciton-polaritons. These particles inherit a sharp energy dispersion of cavity photons and strong interaction nonlinearities of excitons. The bosonic nature of the cavity polaritons allows to observe a number of coherent phenomena such as stimulated scattering of exciton polaritons, polariton parametric oscillators and other. The lower dispersion branch of the exciton polaritons has a sharp minimum and flat wings, which allows for the parametric process, when two pump polaritons scatter into the signal and idler states. We investigate theoretically the optical parametric oscillator based on semiconductor cavity exciton polaritons under a supershort pulsed excitation, which gives the initial state. We consider a typical experimental situation when the pump polaritons are excited in the lower branch of dispersion law under the “magic” angle. We consider the process of the parametric scattering of two pumped polaritons into the signal and idler states. Taking into account the process of polariton-polaritjn scattering we obtained the system of nonlinear equations for the densities of pump, signal and idler states. We obtained two integrals of motion for the densities of the pump, signal and idler states. The solutions of these equations describe the periodical oscillation of the densities of polaritons. The amplitude and period of oscillations depend very strongly on the parameters of the system and especially on the initial densities of the states. We considered the degenerate and nondegenerate cases of the system. We have investigated in detail all peculiarities of the densities time evolution and gave the interpretation of the obtained results. From the equations for amplitudes of the pump, signal and idler modes we can see that the process of stimulated scattering takes place only in the case when the initial densities of two kinds of the polaritons not equal to zero. We predict that there are two distinct types of solutions for the initial phase difference 0 q equals p / 2 or zero. If the 0 / 2 q =p we obtain the oscillating behavior of the densities of polaritons in time, where the period and amplitude of oscillations depend on the initial densities of polaritons. If two kinds of polaritons have the equal density the time evolution is aperiodical one. The period of oscillations decreases with the increasing of the imbalance of initial densities. If the initial phase difference 0 q is equal to zero we obtain a new kind of oscillation with zero amplitude but nonzero period. This is the rest regime, when all the initial densities are nonzero and different, but they have the definite link. The density of polaritons oscillates above or under the definite level, on which the oscillations are absent. We also consider the interpolariton interaction on the time evolution of the system and have obtained new bifurcations, which change the character of the time evolution of the system. We predict the selftrappinglike phenomena. If the parameter of polariton-polariton interaction increases we obtain the bifurcation phenomenon, which divide the evolution of the system into two different behaviors. All obtained solutions of the system of equations are expressed in terms of elliptical functions.