A novel technique for bias suppression within acoustic feedback cancellation systems is proposed. This is achieved based on the use of all-pass filters in the forward part of the hearing aid. The poles of these filters are made time-varying, which results in a frequency response with constant magnitude and varying phase. This is a desired feature of the proposed approach, since the results from human psychoacoustics show that the human ear is not sensitive to moderate phase perturbations. The derivation of the proposed algorithms for the time variation of the location of the poles of all pass filters is based on a rigorous analysis of the phenomenon of bias in acoustic systems. Practical issues, such as the dependence of the steady-state error on the order of the all-pass filter, the number of varying poles, and their standard deviation are examined and strategies for the variation of the poles are introduced. Results obtained from a simulated hearing aid are provided to support the analysis. The quality of the processed audio signals is evaluated through subjective tests.