When the head is free to move, microstimulation of the primate superior colliculus (SC) evokes coordinated movements of the eyes and head. The similarity between these stimulation-induced movements and visually guided movements indicates that the SC of the primate is involved in redirecting the line of sight (gaze). To determine how movement commands are represented by individual collicular neurons, we recorded the activity of single cells in the deeper layers of the superior colliculus of the rhesus monkey during coordinated eye-head gaze shifts. Two alternative hypotheses were tested. The "separate channel" hypothesis states that two displacement commands are generated by the SC: one signal specifying the amplitude and direction of eye movements and a second signal specifying the amplitude and direction of head movements. Alternatively, a single gaze displacement command could be generated by the SC ("gaze displacement" hypothesis). The activity of collicular neurons was examined during three behavioral dissociations of gaze, eye, and head movement amplitude and direction (metrics). Subsets of trials were selected in which the amplitude and direction of either gaze shifts or eye movements or head movements were relatively constant but the metrics of the other two varied over wide ranges. Under these conditions, the separate channel and gaze displacement hypotheses make differential predictions about the patterns of SC activity. We tested these differential predictions by comparing observed patterns with predicted patterns of neuronal activity. We obtained data consistent with the predictions of the gaze displacement hypothesis. The predictions of the separate channel hypothesis were not confirmed. Thus microstimulation data, single-unit recording data, and behavioral data are all consistent with the gaze displacement hypothesis of collicular function--the hypothesis that a gaze displacement signal is derived from the locus of activity within the motor map of the SC and subsequently is decomposed into separate eye and head displacement signals downstream from the colliculus.