Supporting quality of service (QoS) in wireless networks has been a very rich and interesting area of research. Many significant advances have been made in supporting QoS in single wireless networks. However, support for the QoS across multiple heterogeneous wireless networks will be required in the future wireless networks. In connections spanning multiple wireless networks, the end-to-end QoS will depend on several factors such as mobility patterns, connection patterns, and the QoS policies in each of the networks. In this paper, we present several factors that will significantly affect the end-to-end QoS across multiple heterogeneous wireless networks. We present an architecture for multiple heterogeneous wireless networks, several QoS schemes, an analytical model, a simulation model and several interesting results. The simulation model that we have developed can evaluate the QoS performance under a variety of network configurations, user and mobility types, and network resources. Our results show that end-to-end QoS depends on several factors including system utilization, mobility levels, and the individual QoS schemes implemented in individual networks.