This thesis investigates a particular approach, called state-transition specification, to the problem of describing the behavior of modules in a distributed or concurrent computer ,stem. A state-transition specification consists off (1) a state machine, which incorporates the safety or invariance properties of the module, and (2) validity conditions on the computations of the machine, which'capture the desired liveness or eventu;lity properties. The theory and techniques of state. transition specification are developed'from first principles to a point at which it is possible to write example sPeCificatiOns,'to check-the Specifications for coraiatency, and to perform correctlse examples.