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In this work we present, in Chapter I, some results about existence, uniqueness, Continuation and continuous dependence upon initial data, of the solutions of systems of integro-differential equations of' Mnetype x'(t) = f(t,x(t)) + ∫^t_ag(t,s,x(s))ds. Then, in Chapter 11, we use the above mentioned results to present an extension of Wazewski's topological principle for these equations, following the ideas of N. Onuchic's work [af], whiche is devoted to retarded functional differential equations., Chapter III is devoted to some applications of the method presented in Chapter II to the study of the behavior of the solutions.of systems of second order, including the systems with repulsive forces. These application's are based on the works of V.D. 'Fiédorov . Also, in this chapter, we present some results about the, asymptotic behavior of solutions of systems of integro- differential of second order, due to N.Onuchic the case of retarded functional-differential equations.