In xDSL technology, high-speed data are transferred between the central office and the customers, or between two or more central offices using unshielded telephone lines. A major impairment that hinders the increase in data-rate through the twisted-pair line is nearend crosstalk (NEXT) between the adjacent twisted pairs. DSL systems with overlapping transmit and receive spectra are susceptible to NEXT which significantly increases the interference noise in the received signal and also reduces the reliability and availablity of the system. One way to cancel the NEXT in the received signal is to deploy adaptive filters. However, if adaptive filters are deployed to cancel every possible NEXT signal from the other twisted pairs, the computational complexity increases in proportion to N2 where N is the number of twisted pairs in the bundle and, therefore, it becomes prohibitive even for small values of N. In this dissertation, four new methods for NEXT reduction are proposed. The methods aim at reducing computational complexity while maintaining speed and performance. In Chapter 3 an efficient NEXT cancellation system is proposed. The new system first detects the NEXT signals present in the received signal and then assigns adaptive filters to cancel the most significant NEXT signals detected. The detection process uses a fast and efficient algorithm that estimates the crosscorrelation between the transmitted and received signal. By subtracting the adaptive filter estimates of the NEXT signals that have been detected and assigned adaptive filters for cancellation, the magnitude of smaller NEXT signals can be estimated more accurately during the NEXT detection stage. The new system offers an overall computational complexity of order N. This represents a large reduction in the computational effort relative to that in previous NEXT cancellation system which offer computational complexities of order N2. In Chapter 4, the NEXT cancellation system proposed in Chapter 3 is implemented using frequency-domain least-mean-square (FDLMS) adaptive filters to cancel the NEXT signals. Several schemes for assigning the adaptive filter step sizes are explored. It has been found that by making the step sizes proportional to the magnitude of the NEXT signals during the initial phases of adaptation and then making them all equal during the later phases, the convergence rate can be significantly improved. And by returning after convergence to step sizes that are proportional to the magnitudes of the NEXT signals, a much better tracking performance is achieved. In Chapter 5, a new technique that reduces the computational complexity in adaptive filters for NEXT cancellation is proposed. In this technique, the filter length of each adaptive filter is adjusted according to the strength of the NEXT signal. Since the NEXT signals from the other twisted pairs are typically of different magnitudes, using such a technique leads to a significant reduction in the total number of filter taps when compared with fixedlength adaptive filters. The NEXT cancellation is started by using adaptive filters with minimum filter lengths. As the adaptation progresses, the filter length of each adaptive filter is adjusted according to the magnitude of the NEXT signal. Upon convergence, another algorithm is deployed which readjusts the filter lengths of those adaptive filters that are too long or too short. Chapter 6 deals with another new method to mitigate NEXT based on a wavelet denoising technique. In xDSL systems, the received signal typically has greater power in the lower end of the frequency spectrum whereas the NEXT signal has greater power in the higher end. The wavelet technique takes advantage of the difference between the power spectrum of the received signal and that of the NEXT to mitigate the crosstalk noise. In addition, the method has a low computational complexity which makes it fast, efficient, and well suited for high data-rate applications.