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A long-running transaction is an interactive component of a distributed system which must be executed as if it were a single atomic action. In principle, it should not be interrupted or fail in the middle, and it must not be interleaved with other atomic actions of other concurrently executing components of the system. In practice, the illusion of atomicity for a long-running transaction is achieved with the aid of compensation actions supplied by the original programmer: because the transaction is interactive, familiar automatic techniques of check-pointing and roll-back are no longer adequate. This paper constructs a model of long-running transactions within the framework of the CSP process algebra, showing how the compensations are orchestrated to achieve the illusion of atomicity. It introduces a method for declaring that a process is a transaction, and for declaring a compensation for it in case it needs to be rolled back after it has committed. The familiar operator of sequential composition is redefined to ensure that all necessary compensations will be called in the right order if a later failure makes this necessary. The techniques are designed to work well in a highly concurrent and distributed setting. In addition we define an angelic choice operation, implemented by speculative execution of alternatives; its judicious use can improve responsiveness of a system in the face of the unpredictable latencies of remote communication. Many of the familiar properties of process algebra are preserved by these new definitions, on reasonable assumptions of the correctness and independence of the programmer-declared compensations.