The Available Bit Rate (ABR) service in ATM networks has been specified to allow fair and efficient support of data applications over ATM utilizing capacity left over after servicing higher priority classes. One of the architectural features in the ABR specification [tm4] is the Virtual Source/Virtual Destination (VS/VD) option. This option allows a switch to divide an end-to-end ABR connection into separately controlled ABR segments by acting like a destination on one segment, and like a source on the other. The coupling in the VS/VD switch between the two ABR control segments is implementation specific. In this paper, we model a VS/VD ATM switch and study the issues in designing coupling between ABR segments. We identify a number of implementation options for the coupling. A good choice significantly improves the stability and transient performance of the system and reduces the buffer requirements at the switches.