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We describe and analyze a computational model of neural circuits in the mammalian spinal cord responsible for generating and shaping locomotor-like oscillations. The model represents interacting populations of spinal neurons, including the neurons that were genetically identified and characterized in a series of previous experimental studies. Here, we specifically focus on the ipsilaterally projecting V1 interneurons, their possible role in the spinal locomotor circuitry, and their involvement in the generation of locomotor oscillations. The proposed connections of these neurons and their involvement in different neuronal pathways in the spinal cord allow the model to reproduce the results of optogenetic manipulations of these neurons under different experimental conditions. We suggest the existence of two distinct populations of V1 interneurons mediating different ipsilateral and contralateral interactions within the spinal cord. The model proposes explanations for multiple experimental data concerning the effects of optogenetic silencing and activation of V1 interneurons on the frequency of locomotor oscillations in the intact cord and hemicord under different experimental conditions. Our simulations provide an important insight into the organization of locomotor circuitry in the mammalian spinal cord.