One important step towards automated B2B interactions is the enactment of formal and machine understandable B2B conversations. Current standardization efforts allow companies with different internal processes to interact. Although these initiatives offer a certain degree of flexibility they are rather limited because of the pure syntactic approach considered. The use of a formally described language such as Conversation-oriented Process Language (COOL), grounded on well-defined conceptual model and execution semantics, incorporating a history of the conversation and a set of languages depending on the complex of the converstions, would harness the enactment of B2B conversations among trading partners In this paper we present how COOL conversation descriptions between business entities can be executed in a Semantic Web Services execution environment.