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This work consists essentiaily of two parts. In the first part we study the sistem (1) x_j+f_j(x_j, x_j)+g_j(x_j)+h_j + h_j(t,x,x)+k(t,x,x)=0 j=1,2,...,n where x=(x₁,x₂,...,x_n) ∈ Rⁿ. We give sufficient conditions under wich we can guarantee that the origin is globally-asymptoticailly stabie with respect to (1). In the second part we consider the scalar equation (2) x+f(x,x)+g(x) p(x)+h(t,x,x)+k(t,x,x) = 0. We deal with convenient hipotheses related to functions of (2) in order to obtain results on asymptotic stability and global asymptotic stability concerning the origin of (2). The main techniques used in this dissertation are provided by Lyapunov functions, invariance properties of autonomous systems and the theory of Poincare-Bendixson.