Consider a system of differential equations $$ {x^1}{\text{ = }}f(t,x){\text{ }}{{\text{(}}^1}{\text{ = }}\frac{d}{{dt}}) $$ (6.1) . Suppose that f(t,x) e C(I × D,Rn), where I = [0,∞) and D is a connected open set in R. Let F be a class of solutions of (6.1) which remain in D and let x0(t) be an element of F. Setting x = y+x0(t), the system (6.1) is transformed into $$ {y^1}{\text{ = f (t, y + }}{{\text{x}}_0}{\text{ (t)) - f (t,}}{{\text{x}}_0}{\text{ (t))}}{\text{.}} $$ (6.2) If we denote by g(t,y) the right-hand side of (6.2), clearly g(t,0) ≡ 0 and the zero solution y(t) ≡ 0 of (6.2) corresponds to x (t). Therefore it is sufficient to discuss the stability of y(t) ≡ 0 of (6.2) in place of x0(t). For this reason, we assume that f(t,0) ≡ 0 and that D is a domain such that |x| 0.