We have long proposed adaptive sensory-motor modelling as a basis for understanding human movement control and its disorders, in particular stuttering. Several computational theories of movement now take this approach. To be viable, any account of motor behaviour, speech production included, must address three well-known problems: redundancy, limited central resources, and nonlinear interactions. Using state-of-the-art neural adaptive filters we have developed an integrated solution to these difficulties. We discuss this with respect to speech, pointing to how neural models of the interrelationships between efference copy signals and auditory and kinaesthetic feedback signals may pertain to processes of fluency and disfluency.