Seemingly simple behaviors such as swatting a mosquito or glancing at a signpost involve the precise coordination of multiple body parts. Neural control of coordinated movements is widely thought to entail transforming a desired overall displacement into displacements for each body part. Here we reveal a different logic implemented in the mouse gaze system. Stimulating superior colliculus (SC) elicits head movements with stereotyped displacements but eye movements with stereotyped endpoints. This is achieved by individual SC neurons whose branched axons innervate modules in medulla and pons that drive head movements with stereotyped displacements and eye movements with stereotyped endpoints, respectively. Thus, single neurons specify a mixture of endpoints and displacements for different body parts, not overall displacement, with displacements for different body parts computed at distinct anatomical stages. Our study establishes an approach for unraveling motor hierarchies and identifies a logic for coordinating movements and the resulting pose.