This paper deals with nonholonomic perturbed systems. Necessary and sufficient geometric conditions on the perturbation vector field are given in order to put the system into a perturbed one-chained form. Two different sliding mode control strategies are then designed to robustly stabilize, under some conditions, this chained system: one providing a practical stabilization, the other performing a finite time convergence. As a way of illustration, simulations on the example of the unicycle-type mobile robot are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.