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We shall inVestigate the asymptotic relationsHips between the solutions of the nonlinear differential equation. (1) x = f(t,x) and the solutions of the nonlinear perturbed functional differential equation (2) y = f(t,y) + g(t,y_t). The main idea is to extend results of a paper by Fennel and Procter, quoted in the work, converning the ordinary differential equation y = f(t,y) + g(t,y). Our technique is provided by a comparison principle and the fixed point theorem of Schauder-Tychonoff.