The rapid growth of wireless services and mobile users drives a great interest in cellular networks with a hierarchical structure. Hierarchical cellular networks (HCNs) can provide high system capacity, efficient channel utilization and inherent load-balancing capability. In this paper, a two-layer hierarchical cellular network with bidirectional overflow and take-back strategies under generally distributed cell residence times is considered. An analytical model and a performance analysis method are developed, and a number of important performance measures are evaluated. The developed model and analysis method can be easily extended to multi-layer HCNs