Neurons in the auditory cortex exhibit distinct frequency tuning to the onset and offset of sounds, but the cause and significance of ON and OFF receptive field (RF) organisation are not understood. Here we demonstrate that distinct ON and OFF frequency tuning is largely absent in immature mouse auditory cortex and is thus a consequence of cortical development. Simulations using a novel implementation of a standard Hebbian plasticity model show that the natural alternation of sound onset and offset is sufficient for the formation of non-overlapping adjacent ON and OFF RFs in cortical neurons. Our model predicts that ON/OFF RF arrangement contributes towards direction selectivity to frequency-modulated tone sweeps, which we confirm by neuronal recordings. These data reveal that a simple and universally accepted learning rule can explain the organisation of ON and OFF RFs and direction selectivity in the developing auditory cortex.