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In this work we consider three parts. In the first one we develop certain basic facts on functional differential equations with time delay. ln the second part, by using Liapunov Functions, we study the eventually uniform-bounded and uniform stability of a system of ordinary differential equations: y = f(t,y) + g(t,y) . perturbed from the non-linear system x = f(t,x) under the assumption that this system has at least onde bounded solution. The central part of the work is the third one where we extend the above results to functional differential equations - with time delay with an application to the equation x(t) = - ∫⁰_-r = a(-θ)h(Φ (θ))d.