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We shall investigate some of the asymptotic relation- ships between the solutions of the nonlinear functional differential equation (1') x(t) = A(t)x(t) + f(t, x_t and the solutions of the linear ordinary differential equation (2) y(t) = A(t)y(t) These results extend and improve known results of Hallam, Ladas and Lakshnikantham. We also study the asymptotic manifold of solutions of (1') generated by the solutions of (2) extending known results from Ladas, Lakshmikantham and Leela from ordinary differential equations. Our techniques are a combination of a new comparison principle which relates the solutions of the system of functional differential equations z'(t) = F(t, z_tt) to the solutions of a scalar functional differential equation u(t) = g(t, u_t) and the Schauder-Tychonoff fixed phint Theorem.