These services presents course grain business services that encapsulates and abstracts the complexities of the technical implementation underneath. Business processes are created, maintained and executed here. process services are likely to be made up of many different products.
One example of  the products involved in this service layer is Websphere process server. Websphere process will host the business process developed. Once deployed we can start/stop/manage the business process. One example is Loan Application.
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The important terms you hear in this services are business process flows and business state machines.
A business process is the flow or progression of activities, each of which represents the work of a person, an internal system, or the process of a partner company toward some business goal.
A state machine is an event driven business application in which external operations trigger changes that guide the state machine from one discrete mode to another. Each mode is an individual state, and this mode determines what activities and operations can occur

We will discuss Process server indetail after we finish the SOA Foundation explanation.