The authors show that the \(h\)-stability for certain nonlinear difference systems can be studied by using some associated variational systems, extending in this way previous results by R. Medina and M. Pinto [Stability of nonlinear difference equations, Ladde, G. S. (ed.) et al., Dynamic systems and applications. Vol. 2. Proceedings of the 2nd international conference, Morehouse College, Atlanta, GA, USA, May 24–27, 1995. Atlanta, GA: Dynamic Publishers. 397–404 (1996; Zbl 0861.39004)]. Then, it is shown that the \(h\)-stability properties persist under certain perturbations of the system.