Key points Quadrupeds express different gaits depending on speed of locomotion. Central pattern generators (one per limb) within the spinal cord generate locomotor oscillations and control limb movements. Neural interactions between these generators define interlimb coordination and gait. We present a computational model of spinal circuits representing four rhythm generators with left–right excitatory and inhibitory commissural and fore–hind inhibitory interactions within the cord. Increasing brainstem drive to all rhythm generators and excitatory commissural interneurons induces an increasing frequency of locomotor oscillations accompanied by speed‐dependent gait changes from walk to trot and to gallop and bound. The model closely reproduces and suggests explanations for multiple experimental data, including speed‐dependent gait transitions in intact mice and changes in gait expression in mutants lacking certain types of commissural interneurons. The model suggests the possible circuit organization in the spinal cord and proposes predictions that can be tested experimentally. Abstract As speed of locomotion is increasing, most quadrupeds, including mice, demonstrate sequential gait transitions from walk to trot and to gallop and bound. The neural mechanisms underlying these transitions are poorly understood. We propose that the speed‐dependent expression of different gaits results from speed‐dependent changes in the interactions between spinal circuits controlling different limbs and interlimb coordination. As a result, the expression of each gait depends on (1) left–right interactions within the spinal cord mediated by different commissural interneurons (CINs), (2) fore–hind interactions on each side of the spinal cord and (3) brainstem drives to rhythm‐generating circuits and CIN pathways. We developed a computational model of spinal circuits consisting of four rhythm generators (RGs) with bilateral left–right interactions mediated by V0 CINs (V0D and V0V sub‐types) providing left–right alternation, and conditional V3 CINs promoting left–right synchronization. Fore and hind RGs mutually inhibited each other. We demonstrate that linearly increasing excitatory drives to the RGs and V3 CINs can produce a progressive increase in the locomotor speed accompanied by sequential changes of gaits from walk to trot and to gallop and bound. The model closely reproduces and suggests explanations for the speed‐dependent gait expression observed in vivo in intact mice and in mutants lacking V0V or all V0 CINs. Specifically, trot is not expressed after removal of V0V CINs, and only bound is expressed after removal of all V0 CINs. The model provides important insights into the organization of spinal circuits and neural control of locomotion.