We previously reported that visuomotor activity in the superior colliculus (SC) – a key midbrain structure for the generation of rapid eye movements – preferentially encodes target position relative to the eye (Te) during low-latency head-unrestrained gaze shifts (DeSouza et al., 2011). Here, we trained two monkeys to perform head-unrestrained gaze shifts after a variable post-stimulus delay (400–700 ms), to test whether temporally separated SC visual and motor responses show different spatial codes. Target positions, final gaze positions and various frames of reference (eye, head, and space) were dissociated through natural (untrained) trial-to-trial variations in behaviour. 3D eye and head orientations were recorded, and 2D response field data were fitted against multiple models by use of a statistical method reported previously (Keith et al., 2009). Of 60 neurons, 17 showed a visual response, 12 showed a motor response, and 31 showed both visual and motor responses. The combined visual response field population (n = 48) showed a significant preference for Te, which was also preferred in each visual subpopulation. In contrast, the motor response field population (n = 43) showed a preference for final (relative to initial) gaze position models, and the Te model was statistically eliminated in the motor-only population. There was also a significant shift of coding from the visual to motor response within visuomotor neurons. These data confirm that SC response fields are gaze-centred, and show a target-to-gaze transformation between visual and motor responses. Thus, visuomotor transformations can occur between, and even within, neurons within a single frame of reference and brain structure.