In this paper, we investigate the connection admission control problem in mobile personal communications networks. In contrast to other studies on this aspect which either focused on only single-class call connections or ignored user mobility, our study directly addresses the connection admission control for multiple-class calls with user mobility. A generic class of coordinate-convex admission control policies is considered. An efficient numerical method is proposed to derive the connection-level quality of service (&OS) and is verified with computer simulation results. The proposed analysis may be employed in a network design tool for studying the admission control policy and selecting system parameters to satisfy the required connection-level &OS.