The current research addresses the hypothesis that certain aspects of sequential cognition have made substantial contributions to the human language processing capability, from a functional neurophysiology perspective. We first describe a cognitive sequence processing model that was developed based on the functional neuroanatomy of primate cortex and basal ganglia. We demonstrate how this model is capable of simulating the behavior of human infants in extracting serial, temporal and abstract structure from language-like sound sequences as revealed in recent psycholinguistic experiments. We then demonstrate how, through training, this model can perform adult level syntactic comprehension, based on dissociated processing streams for open vs. closed class words. The model subsequently predicts: (1) that impaired syntactic processing (as in agrammatic aphasia) will be associated with impairments in corresponding non-linguistic cognitive sequencing tasks, and (2) that neurophysiological processes (as revealed by ERPs) involved in syntactic processing should also be involved in the corresponding non-linguistic cognitive sequencing tasks. Data confirming these predictions are reviewed. We conclude that the study of sequential cognition will provide a new paradigm for the investigation of the neurophysiological bases of language.