Web services have a potential to enhance B2B e-commerce over the Internet by allowing companies and organizations to publish their business processes on service directories where potential trading partners can find them. This can give rise to new business paradigms based on ad-hoc trading relations as companies, particularly small to medium scale, can cheaply and flexibly enter into fruitful contracts, e.g., through subcontracting from big companies by simply publishing their business processes and the services they offer. More business process support by the web service infrastructure is however needed before such a paradigm change can materialize. A service for searching and matchmaking of business processes does not yet exist in the current infrastructure. We believe that such a service is needed and will enable companies and organizations to be able to establish ad-hoc business relations without relying on manually negotiated frame contracts like RosettaNet PIPs. This paper gives a formal semantics to business process matchmaking and an operational description for matchmaking.