The incorporation of Gallium Nitride (GaN) Power Amplifiers (PAs) into future high power aperture radar systems is certain; however, the introduction of this technology into multifunction radar systems will present new challenges to radar engineers. This dissertation describes a broad investigation into amplitude and phase transients produced by GaN PAs when they are excited with multifunction radar waveforms. These transients are the result of self-heating electrothermal memory effects and are manifested as interpulse instabilities that can negatively impact the coherent processing of multiple pulses. A behavioral model based on a Foster network topology has been developed to replicate the measured amplitude and phase transients accurately. This model has been used to develop a digital predistortion technique that successfully mitigates the impact of the transients. The Moving Target Indicator (MTI) Improvement Factor and the Root Mean Square (RMS) Pulse-to-Pulse Stability are used as metrics to assess the impact of the transients on radar system performance and to test the effectiveness of a novel digital predistortion concept. / Ph. D.