Perceptual constancy requires the brain to maintain a stable representation of sensory input. In the olfactory system, activity in primary olfactory cortex (piriform cortex) is thought to determine odour identity1-5. Here we present the results of electrophysiological recordings of single units maintained over weeks to examine the stability of odour-evoked responses in mouse piriform cortex. Although activity in piriform cortex could be used to discriminate between odorants at any moment in time, odour-evoked responses drifted over periods of days to weeks. The performance of a linear classifier trained on the first recording day approached chance levels after 32 days. Fear conditioning did not stabilize odour-evoked responses. Daily exposure to the same odorant slowed the rate of drift, but when exposure was halted the rate increased again. This demonstration of continuous drift poses the question of the role of piriform cortex in odour perception. This instability might reflect the unstructured connectivity of piriform cortex6-12, and may be a property of other unstructured cortices.