The timing behavior of a real-time system depends not only on delays due to process synchronization, but also on the availability of shared resources. Most current real-time models capture delays due to process synchronization; however, they abstract out resource-specific details by assuming idealistic operating environments. On the other hand, scheduling and resource allocation algorithms used for real-time systems ignore the effect of process synchronization except for simple precedence relations between processes. To bridge the gap between these two disciplines, we have developed a formalism called Communicating Shared Resources, or CSR. This paper presents the priority-based process algebra called the Calculus for Communicating Shared Resources (CCSR), which provides an equational characterization of the CSR language. The computation model of CCSR is resource-based in that multiple resources execute synchronously, while processes assigned to the same resource are interleaved according to their priorities. CCSR possesses a prioritized strong equivalence for terms based on strong bisimulation. The paper also describes a producer and consumer problem whose correct timing behavior depends on priority.