This paper describes the discourse component of GALAXY, a multidomain, multimodal conversational system. In designing this module, we are attempting to develop domain-independent mechanisms, controlled via declarative tables, to promote convenient instantiation of a discourse component for each new domain. Direct anaphoric reference as well as elliptical reference are dealt with appropriately. Users can also refer verbally to items selected via mouse clicks. Cross domain references are particularly challenging, as is the ambiguity problem arising from different case roles for different subdomains. Users often utter fragments, sometimes in response to serverinitiated dialogue exchanges, so an extensive fragment interpretation mechanism is supported.