Development of linear modulation schemes has opened the way for spectrally efficient, high speed digital communication systems for voice and data applications. A trend has been to develop ultra wide and wide bandwidth modulation formats, which has meant feedback linearisation schemes (both analogue and digital) are no longer effective. This has in turn led to a number of approaches that involve predistorting the signal prior to amplification, with a characteristic that is the inverse to that of the power amplifier (PA). This thesis presents a polynomial based predistortion for linearisation of an RF PA. The predistortion characteristic is adaptive, using the LMS algorithm to minimise the mean squared error between output of the PA, and a scaled version of the baseband signal. This system can reduce third-order intermodulation by 40 dB when running in real time.