Consideration was given to the discontinuous (pulse) dynamic system on plane which obeys an ordinary autonomous system of differential equations of the first order and the law of skip x→ F(x) of the phase point occurring as soon as the point reaches the critical line M. It was assumed that the origin O was the stationary point of the original system of equations, the line M passed through O, F(O) ＝ O, and the discontinuous system was structurally stable within some neighborhood of the point O. Under these assumptions, efficient necessary and sufficient conditions for asymptotic stability of the point O both relative to its full neighborhood and some sectors with centers at O were obtained.
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