An adaptive noise canceling (ANC) circuit adaptively generates an anti-noise signal that is injected into the speaker or other transducer output to cause cancellation of ambient audio sounds. At least one microphone provides an error signal indicative of the noise cancellation at the transducer, and the adaptive filter is adapted to minimize the error signal. In order to prevent improper adaptation or instabilities in one or both of the adaptive filters, spikes are detected in the error signal by comparing the error signal or its rate of change to a threshold. Therefore, if the magnitude of the coefficient error is greater than a threshold value for an update, the update is skipped. Alternatively the step size of the updates may be reduced. Similar criteria can be applied to a filter modeling the secondary path, based on detection applied to both the source audio and the error signal.