In quadrupeds, a unique form of memory is used to guide the hind legs over barriers that have already been stepped over by the forelegs. This memory is very long-lasting (many minutes), incorporates precise information about the size and position of the barrier relative to the hind legs, and is updated as the animal steps sequentially across a barrier. Recent findings from electrophysiological and lesion studies have revealed that neuronal systems in the parietal cortex are necessary for establishing the long-lasting feature of the memory and may be involved in representing the current position of the barrier relative to the moving body. We hypothesize that the latter involves the modulation of activity in neuronal systems in the posterior parietal cortex by efference copy signals of motor commands for stepping and by sensory signals from muscle proprioceptors. We propose that motor pattern generation for walking occurs within a framework of a body schema that constantly informs pattern generating networks about the geometry of the body and the location of near objects relative to the body.