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In this work we study the relative asymptotic equivalence between the solutions of a system d/dt Dxt_t = f(t, x_t (L) and its perturbed d/dt [Dx_t - G (t, x_t)] = f(t,x_t) + g(t, x_t) (P). We give an extension of the Alekseev variation of constant formula for neutral nonlinear perturbed equation and make an application to the relative asymptotic equivalence between the solutions of (L) and (P). We study also different concepts of relative asymptotic equivalence in different cases when D and f are linear autonomous and nonlinear nonautonomous. The techniques employed are concerned vvith the variation of constants formula, comparison methods and functional analysis methods as for example the Banach and Darbo fixed point theorems and uniform boundedness principle.