In this paper we study TCP performance in the presence of vertical handoffs between access networks with widely varying link characteristics. TCP being an end-to-end protocol has performance problems as its behaviour depends on the end-to-end path characteristics which are likely to be affected by a vertical handoff. We carry out a systematic study of TCP behaviour and the consequent problems that arise in various handoff scenarios between networks with different bandwidth and delay characteristics. This study can serve as a basis to evaluate any modifications to the TCP algorithm to adapt to a vertical handoff.