In this paper, the notions of SNS-invariance and SNS-domain of attraction are introduced. The SNS-domain of attraction serves as an estimation of the domain of attraction of a saturated system. It is shown that, in the case of single input saturated systems, any contractive set is contained in the SNS-domain of attraction. Another important characteristic of the SNS-domain of attraction is that it contains any estimation obtained by means of a linear difference inclusion of the saturated system. A simple algorithm that converges to the SNS-domain of attraction is presented. An illustrative example is given. (C) 2006 Elsevier Ltd. All rights reserved.