Service-oriented architecture (SOA) is an architecture paradigm targeting integration of applications within and across enterprise boundaries. It has gathered research and industry acceptance and has given an enormous impetus to the business process management technology. Web service (WS) technology is one implementation of the SOA paradigm. It enables seamless integration of new and legacy applications through a stack of standardized composable specifications. WS orchestration is facilitated by the Business Process Execution Language which provides a recursive service composition model. While the programming model the WS technology provides is very flexible, a major deficiency is the need to discover services implementing a particular abstract interface, whereas functional similarities of services are disregarded. The Semantic Web Service technologies, like Web Service Modelling Ontology (WSMO) and Web Ontology Language for Services have been developed with the purpose of eliminating these deficiencies by enabling service discovery based on functional and non-functional properties. The paper aims to focus on these issues. This paper presents a list of requirements that business processes impose on SOA applications. It analyzes the support that WSMO/Web Service Model eXecution environment (WSMX) provides to address these requirements and compares it with the support enabled by the WS specification stack. The paper identifies major flaws in the WSMO model and its reference implementation with respect to business process support. The paper recommends possible solutions for eliminating the lack of needed features on behalf of WSMO/WSMX. It presents in detail how to enable asynchronous stateful communication among WSMO WS and partner-based WS discovery by extending the WSMO model. Additionally, it extends the API of the reference implementation to facilitate the execution of services communicating asynchronously.