1. A method of stateful business application processing in an otherwise stateless service-oriented architecture (‘SOA’), the SOA comprising SOA services, each SOA service carrying out a processing step of a business application, the method comprising: configuring each service of the SOA to record state information describing a state of the service upon completion of a processing step in the business application and providing the state information to a subsequent service; and executing the business application in the SOA, including sending requests for data processing among the services, each such request comprising a specification of a state of the executing business application; wherein the SOA and the SOA services used to execute the business application are stateless when not executing the business application; wherein the SOA and the SOA services used to execute the business application are stateful when executing the business application wherein executing the business application in the SOA includes each service carrying out a processing step of the business application; wherein carrying out a processing step includes processing data in dependence upon the state of the business application; wherein sending requests for data processing among the services further comprises sending requests for both forward processing and reverse processing of the processing steps of the business application, wherein forwarding processing is the processing of data in the business application in one state to a later state, wherein reverse processing is the processing of data in the business application in one state to an earlier state; wherein the state of the business application included in the request implicitly identifies the request as for either forward processing or reverse processing of the processing steps of the business application; wherein the web services are described in WSDL and registered in at least one UDDI directory; and wherein the business application comprises a software application that provides business functionality in the SOA.