The computational role of cortical layers within auditory cortex has proven difficult to establish. One hypothesis is that interlaminar cortical processing might be dedicated to analyzing temporal properties of sounds; if so, then there should be systematic depth-dependent changes in cortical sensitivity to the temporal context in which a stimulus occurs. We recorded neural responses simultaneously across cortical depth in primary auditory cortex and anterior auditory field of CBA/Ca mice, and found systematic depth dependencies in responses to second-and-later noise bursts in slow (1-10 bursts/s) trains of noise bursts. At all depths, responses to noise bursts within a train usually decreased with increasing train rate; however, the rolloff with increasing train rate occurred at faster rates in more superficial layers. Moreover, in some recordings from mid-to-superficial layers, responses to noise bursts within a 3-4 bursts/s train were stronger than responses to noise bursts in slower trains. This non-monotonicity with train rate was especially pronounced in more superficial layers of the anterior auditory field, where responses to noise bursts within the context of a slow train were sometimes even stronger than responses to the noise burst at train onset. These findings may reflect depth dependence in suppression and recovery of cortical activity following a stimulus, which we suggest could arise from laminar differences in synaptic depression at feedforward and recurrent synapses.