A control approach for the practical and asymptotic stabilization of nonlinear driftless systems subjected to additive perturbations is proposed. Such perturbations arise naturally, for instance, in the modeling of trajectory stabilization problems for controllable driftless systems on Lie groups. The objective of the approach is to provide practical stability of an arbitrary given point in the state space, whatever the perturbations, and asymptotic stability (resp., convergence to the point) when the perturbations are absent (resp., tend to zero). A general framework is presented in this paper, and a control solution is proposed for the class of the chained systems.