In this paper, we extend the globally convergent steering algorithm for regular nonholonomic systems presented in [7] to a much larger class of systems which contain singularities. This extension is based on the construction of a continuous first order approximation of the control system. We also propose an exact motion planning method for nilpotent systems. The method makes use of sinusoidal control laws and generalizes the algorithm presented in [12] for steering chained-form systems. It gives rise to C1 trajectories, then makes easy dynamical extension. ©2009 IEEE.