Acoustic feedback is one of the main problems in modern hearing aids. It distorts the desired signal and limits the maximum stable gain. Results on acoustic feedback cancellation systems based on the prediction error method of closed-loop identification indicate that they perform better than most alternative solutions. Most available analyses of such systems, however, are limited to steady-state results. This paper presents a transient mean-square analysis of a recently proposed system. The structure is analyzed for slow adaptation and for autoregressive input signals. Analytical models are derived for the mean and mean-square adaptive weight behaviors. This includes a model for the transient behavior of the bias in the feedback path estimator. Monte Carlo simulations are presented to verify the accuracy of the derived models.