The report is devoted to the study of higher order time integration methods for multibody systems with unilateral constraints. After a brief presentation of the mathematical modelling of nonsmooth multibody systems, several estimates on the local error of consistency of the Moreau time--stepping scheme are given. Based on these estimates, an attempt at an adaptive time--step strategy is presented on academic examples. Finally, higher order event--capturing methods are designed by coupling implicit Runge--Kutta schemes and the Moreau's time--stepping scheme.