Feedback cancellation apparatus uses a cascade of two filters along with a short bulk delay. The first filter is adapted when the hearing aid is turned on in the ear. This filter adapts quickly using a white noise probe signal, and then the filter coefficients are frozen. The first filter models parts of the hearing-aid feedback path that are essentially constant over the course of the day. The second filter adapts while the hearing aid is in use and does not use a separate probe signal. This filter provides a rapid correction to the feedback path model when the hearing aid goes unstable, and more slowly tracks perturbations in the feedback path that occur in daily use. The delay shifts the filter response to make the most effective use of the limited number of filter coefficients.