When multiple arms are used to manipulate a large object, it is necessary to maintain and control contacts between the object and effector(s) on one or more arms. The contacts are characterized by holonomic as well as nonholonomic constraints. This paper addresses the control of mechanical systems subject to nonholonomic constraints, rolling constraints in particular. It has been shown that such a system is always controllable, but cannot be stabilized to a single equilibrium by smooth feedback [l, 2]. In this paper, we show that the system is not input-state linearizable though input-output linearization is possible with appropriate output equations. Further, if the system is position-controlled (i.e., the output equation is a functions of position variables only), it has a zero dynamics which is Lagrange stable but not asymptotically stable. We discuss the analysis and controller design for planar as well as spatial multi-arm systems and present results from computer simulations to demonstrate the theoretical results.