Adaptive filtering is an important topic in modern signal processing. LMS algorithm is the most widely used for adaptive filtering because of its simplicity and stability. On the other hand, wavelet transform is a block I transform that gives a powerful representation of signals. The work in this thesis combines the Wavelet Packet Transform (WPT) with the LMS adaptive filter. Two structures of wavelet packet transform were simulated for system modeling applications as a representative of many adaptive filtering applications. The first structure is a transform domain adaptive filter. This structure was compared with transform-domain adaptive filter based DCT and NLMS algorithm. Learning curves were obtained for optimum step size and up to three decomposition levels. The Daubechies family was used in this structure. The second structure is the subband adaptive filter based on the WPT. This structure was used for system modelling also. NLMS algorithm was used to update the weights of the adaptive filter. The Daubechies family was used in the analysis and synthesis filter bank. Learning curves were obtained for up to three decomposition levels and compared with NLMS.This system was used as an adaptive echo canceller to model echo path of length 400 tap. The simulation work was carried out on a PC with PI 233MHz processor and programmed using MATLAB simulation package version 6.