Recent studies have established and characterized the propagation of traveling electrical waves along the cat spinal cord during scratching, but the neuronal architecture that allows for the persistence of such waves even during periods of absence of bursts of motoneuron activity (deletions) is still unclear. Here we address this problem both theoretically and experimentally. Specifically, we monitored during long lasting periods of time the global electrical activity of spinal neurons during scratching. We found clear deletions of unaltered cycle in extensor activity without associated deletions of the traveling spinal wave. Furthermore, we also found deletions with a perturbed cycle associated with a concomitant absence of the traveling spinal wave. Numerical simulations of an asymmetric two-layer model of a central-pattern generator distributed longitudinally along the spinal cord qualitatively reproduce the sinusoidal traveling waves, and are able to replicate both classes of deletions. We believe these findings shed light into the longitudinal organization of the central-pattern generator networks in the spinal cord.