Web services offer a number of valuable features towards supporting the development of open distributed systems, built out of the composition of autonomous services. Nonetheless, the resulting systems must offer a number of non-functional properties and in particular dependability-related ones, for acceptance by users, including effective exploitation in the e-business domain. However, dependability of composite services can only be achieved according to the recovery property of composed Web services. This calls for the rigorous specification of the standard and exceptional behavior of Web services. This paper introduces the WS-RESC conversation language that addresses this issue. In a way similar to existing conversation languages, WS-RESC includes constructs for defining ordering and choices. However, WS-RESC further includes constructs for specifying concurrency since it is an inherent feature of distributed systems, and for specifying timing constraints and recovery properties of conversation since these are key behavioral properties in the context of dependability.