A distributed business process organizes activities by several enterprises to fulfill a given business goal. The purpose of this paper is to formalise what it means for such a process to be feasible (possible to carry out given the resources delegated for its execution) and for a feasible process to be correct (satisfying a given business goal), using customer-driven manufacturing as a particular, although broadly defined business area. Possible applications are: formal analysis of business processes, providing formal semantics to process modelling languages, and specification and rigorous development of business-support software.