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In this work we consider three parts. ln the first one we develop certain basic facts on the Invariance Theory for non Autonomous Systems. In the second part, by using Liapunov Functions and the Invariance Theory, we give sufficients conditions to guarantee that every solution of the second order scalar equation (I) x + f(t,x,x ) + g(x).p(x) = 0 considered as a perturbed equation of (II) x + f(t,x,x) + g(x).p(x) = 0, tends to zero, with its derivative, as t → ∞. We also give sufficients conditions to ímply that the solution (x,x) = (0,0) of (I) is globally asymptotically stable. In the third part we extend to Differential Equations like (I),the results obtained in the second part.