Due to increasing competitive pressure, manufacturing companies need to support flexible and scalable business processes - both on the shop floor and in their enterprise software systems. Cloud manufacturing is a recent approach to realize real-world manufacturing processes by applying well-known basic concepts from the field of Cloud computing to this domain. To implement Cloud manufacturing, it is necessary to model, enact and monitor according manufacturing processes and virtualize the single process steps. So far, Business Process Management Systems do not explicitly support Cloud manufacturing. This paper analyzes requirements regarding process enactment for Cloud manufacturing and provides a concept for an according software framework.