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This paper deals with nonlinear oscillations of the torsion oscillator with reciprocal rigidly connected impact masses. It is assumed that two impulses occur at one interval of the disturbing torsion moment. The asymptotic Krilow-Bogolyubov-Mitropolyskiy method is applied, along with the stereomechanical impact theory for the inclusion of impact conditions, to the determination of the primary approximation of the torsion system nonlinear oscillations. Phase trajectories are drawn on the basis of the numerical results. The mathematical model of the vibroimpact system is written in the form of an autonomous nonlinear system of the first order differential equations. The integral curves and the phase trajectories are obtained by means of the Runge-Kutta method, of the Turbo-Pascal program and with the aid of the computer graphics.