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This work has two distincts objectives. However these objectives are basically dependents on the invariance properties of w-limit sets of solutions, bounded in the future, of differential equations. The first objective is essentially an application of the above mentioned result. We look for conditions under which, we can guarantee that every solution (x(t),x(t)), of a nonautonomous second order differential equation. x + h(t,x,x)x + f(x) + g(t,x,X) + p(t,x,x) = O, tends to (η,0), as t → ∞ where (η,0) is an equilibrium point of a certain autonomous equation. We are also interested in studying the stability properties of a class of equilibrium point of the above mentioned second: order differential equation. Our results are closely related to the ones obtained by N,.Onu chic in [11]. However our hypotheses are different from his assumptions. The second main objective of this work is to extend criterions of instability obtained by N.Onuchic [13] to a certain class of nonautonomous differential systems. To this end the main tool used here is provided by results of H.M.Rodrigues [16] on Invariance.