Mobile IP enables TCP session continuity across IP subnets. For mobility across access technologies, however, TCP, which accounts for the transport of the vast majority of data transfer over data networks, is faced with an additional challenge attributed to the different link properties, such as throughput and RTT, of these access technologies. Unaware of the change in access technology, TCP is bound to interpret these sudden variations in link properties incorrectly, and consequently trigger recovery mechanisms that lead to a further deterioration in the handover performance. This paper analyzes the behaviour of TCP during mobility across wireless and cellular access technologies, while there are ongoing sessions. The study concentrates on WLAN and GPRS as examples of these access technologies, respectively, but can easily be extended to cover also other access technologies. The study considers the effect of using different sender and receiver TCP variants, as well as the impact of the duration of the handover procedure. From the results, some issues have been identified, and proposals for solving these issues have been analyzed.