Adaptive filtering is commonly used to cancel feedback signals in hearing aids. Currently, the most popular approach uses direct closed-loop identification with FIR filtering, using variants of the LMS algorithm. The use of an FIR filter to model the feedback path allows flexibilty, but this approach has no prior knowledge of the hearing aid system. This means that the model can often be inaccurate, with the unwanted effects of reduced feedback cancellation and distortion of the desired audio input signal. The aim of this work is to develop a novel adaptive feedback cancellation algorithm that updates the values of physical parameters in a model for the hearing aid system rather than updating filter coefficients. This has the probable advantages of having low order due to the limited number of parameters and of operating within a well-defined range of parameter values corresponding to realistic physical dimensions. Potential benefits include fast convergence, robustness and reduced distortion of the audio input signal. In the first part of this thesis, a two-port network computer model of an in situ in-the-ear hearing aid system was developed, from which simplified analytic expressions for the feedback path response and error surface gradients were derived. The model was fitted to a range of measured feedback path responses using numerical optimisation techniques and the convexity of the error surface was explored, since this would affect the use of steepest descent-based algorithms. A new algorithm was then developed that adapted the estimated values of physical parameters in the model to track and cancel changes in the feedback path. Simulation studies with modelled and measured feedback path data were used to investigate the performance of the parametric adaptive algorithm compared to the NLMS algorithm, showing the potential benefits of this new approach.