We consider discrete-time systems x(k + 1) = Ax(k) + f(x(k)) where the matrix A of the linear part is known and positive, the non-linearity f is unknown but belongs to a class for which A + f'(x) is positive with spectral radius < I for all x is an element of R-n. This, with the additional property that x - Ax - f(x) is proper, is sufficient for global stability of the system. The results are applied to the continuous system x = Ax + B phi(C(T)x) by considering the translation operator along trajectories and studying the resulting discrete system.