More and more companies are outsourcing parts of their business processes to third party providers to exploit the expertise and economies of scale of these third party providers. In the IT field, emerging delivery models for software such as Software as a Service and cloud computing offer the possibility to outsource applications and computing infrastructure and thus enable enterprises to focus on their core competences. In this paper we investigate how the new delivery models affect the outsourcing of business processes modeled in WS-BPEL. WS-BPEL is the standard to model and execute business processes in Web service-based IT landscapes. We describe how security and trust issues affect the execution of BPEL processes in the cloud and show the requirements on the middleware supporting the execution of BPEL processes.