الملخص

In this paper we investigate the existence and approximation of the periodic solution for a system of nonlinear integro -differential equations with retarded argument. The numerical -analytic method has been adapted to study the periodic solutions of the nonlinear ordinary differential equations that were introduced by Samoilenko, This work lead to develop and expand the method, which is mentioned above, and thus the results obtained are more comprehensive that the study mentioned previously in the reference [1].