The REST architectural style has attracted a lot of interest from industry due to the nonfunctional properties it contributes to Web-based solutions. SOAP/WSDL-based services, on the other hand, provide tools and methodologies that allow the design and development of software supporting complex service arrangements, enabling complex business processes which make use of well-known control-flow patterns. It is not clear if and how such patterns should be modeled, considering RESTful Web services that comply with the statelessness, uniform interface and hypermedia constraints. In this article, we analyze a set of fundamental control-flow patterns in the context of stateless compositions of RESTful services. We propose a means of enabling their implementation using the HTTP protocol and discuss the impact of our design choices according to key REST architectural principles. We hope to shed new light on the design of basic building blocks for RESTful business processes. © 2013 ACM.