Central pattern generators (CPGs) are central nervous system (CNS) networks that can generate coordinated output in the absence of patterned sensory input. For decades, this concept was applied almost exclusively to simple, innate, rhythmic movements with essentially identical cycles that repeat continually (e.g. respiration) or episodically (e.g. locomotion). But many natural movement sequences are not simple rhythms, as they include different elements in a complex order, and some involve learning. The concepts and experimental approaches of CPG research have also been applied to the neural control of complex movement sequences, such as birdsong, though this is not widely appreciated. Experimental approaches to the investigation of CPG networks, both for simple rhythms and for complex activity sequences, have shown that: (1) brief activation of the CPG elicits a long-lasting naturalistic activity sequence; (2) electrical stimulation of CPG elements alters the timing of subsequent cycles or sequence elements; and (3) warming or cooling CPG elements respectively speeds up or slows down the rhythm or sequence rate. The CPG concept has also been applied to the activity rhythms of populations of mammalian cortical neurons. CPG concepts and methods might further be applied to a variety of fixed action patterns typically used in courtship, rivalry, nest building and prey capture. These complex movements could be generated by CPGs within CPGs ('nested' CPGs). Stereotypical, non-motor, nonrhythmic neuronal activity sequences may also be generated by CPGs. My goal here is to highlight previous applications of the CPG concept to complex but stereotypical activity sequences and to suggest additional possible applications, which might provoke new hypotheses and experiments.