Abstract Howling caused by feedback in hearing aids reduces comfort and limits the hearing aid amplification. Recent studies investigated adaptive feedback cancellation systems which track the response of the feedback path and attempt to cancel the feedback signal therefore reducing the howling. Since in practice the feedback signal is never cancelled completely, the closed-loop system can still become unstable. This paper presents a formulation of a robust hearing aid system with guaranteed closed-loop stability which is free from howling. The system incorporates an adaptive feedback cancellation filter integrated with a robust compensation filter. The limit on the tracking error of the feedback cancellation filter is first defined, from which a limit on the gain of the compensation filter which guarantees robust stability is derived. Then, an adaptive feedback cancellation algorithm with improved robustness is proposed. A simulation example of adaptive feedback cancellation in a hearing aid with a time-varying acoustic leak is then presented, showing the benefit of the robust-adaptive algorithm.