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Suppose the second-order equation x + g(x, x) = O has a periodic solution x₀ , where g ∈ C². The main concern of this work is to study the existence of periodic solutions of the.perturbed equation &xuml; + g(x, x) = ε (t, x ,x, ε) near x₀ for small lel ,where Ι ε Ι, where f ∈ C¹ and f is a periodic function. In this work we use the Liapunov Schmidt Reduction Method and the Implicit Function Theorem.