Human behavior shows a variety of serially ordered action sequences. This paper presents a theory of serial order which describes how sequences of actions might be learned and performed. In this theory, parallel interactions across time (coarticulation) and parallel interactions across space (dual-task interference) are viewed as two aspects of a common underlying process. It describes a dynamical system which is embodied as a "parallel distributed processing" or "connectionist" network. The trajectories of this dynamical system come to follow desired paths corresponding to particular action sequences as a result of a learning process during which constraints are imposed on the system. These constraints enforce sequentiality where necessary, and as they are relaxed, performance becomes more parallel. The theory is applied to the problem of coarticulation in speech production and simulation experiments are presented. (Author/JAZ)