Different locomotor gaits in mammals, such as walking or galloping, are produced by coordinated activity in neuronal circuits in the spinal cord. Coordination of neuronal activity between left and right sides of the cord is provided by commissural interneurons (CINs), whose axons cross the midline. In this study, we construct and analyse two computational models of spinal locomotor circuits consisting of left and right rhythm generators interacting bilaterally via several neuronal pathways mediated by different CINs. The CIN populations incorporated in the models include the genetically identified inhibitory (V0_D) and excitatory (V0_V) subtypes of V0 CINs and excitatory V3 CINs. The model also includes the ipsilaterally projecting excitatory V2a interneurons mediating excitatory drive to the V0_V CINs. The proposed network architectures and CIN connectivity allow the models to closely reproduce and suggest mechanistic explanations for several experimental observations. These phenomena include: different speed-dependent contributions of V0_D and V0_V CINs and V2a interneurons to left-right alternation of neural activity, switching gaits between the left-right alternating walking-like activity and the left-right synchronous hopping-like pattern in mutants lacking specific neuron classes, and speed-dependent asymmetric changes of flexor and extensor phase durations. The models provide insights into the architecture of spinal network and the organization of parallel inhibitory and excitatory CIN pathways and suggest explanations for how these pathways maintain alternating and synchronous gaits at different locomotor speeds. The models propose testable predictions about the neural organization and operation of mammalian locomotor circuits.