All forms of locomotion are repetitive motor activities that require coordinated bilateral activation of muscles. The executive elements of locomotor control are networks of spinal neurons that determine gait pattern through the sequential activation of motor-neuron pools on either side of the body axis. However, little is known about the constraints that link left-right coordination to locomotor speed. Recent advances have indicated that both excitatory and inhibitory commissural neurons may be involved in left-right coordination. But the neural underpinnings of this, and a possible causal link between these different groups of commissural neurons and left-right alternation, are lacking. Here we show, using intersectional mouse genetics, that ablation of a group of transcriptionally defined commissural neurons--the V0 population--leads to a quadrupedal hopping at all frequencies of locomotion. The selective ablation of inhibitory V0 neurons leads to a lack of left-right pattern at low frequencies, mixed coordination at medium frequencies, and alternation at high locomotor frequencies. When ablation is targeted to excitatory V0 neurons, left-right alternation is present at low frequencies, and hopping is restricted to medium and high locomotor frequencies. Therefore, the intrinsic logic of the central control of locomotion incorporates a modular organization, with two subgroups of V0 neurons required for the existence of left-right alternating modes at different speeds of locomotion. The two molecularly distinct sets of commissural neurons may constrain species-related naturally occurring frequency-dependent coordination and be involved in the evolution of different gaits.