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. / The incorporation of Gallium Nitride (GaN) Power Amplifiers (PAs) into future radar systems is certain, and will present new challenges to radar engineers. This dissertation describes a broad investigation into signal transients produced by GaN PAs when they are excited with a wide variety of RF pulsed waveforms. These waveforms are representative of those used by a radar system to conduct multiple functions or missions. The transients are primarily the result of changes in the GaN PA gain due to self-heating, and are manifested as differences in consecutive pulses. These pulse-to-pulse differences negatively affect the ability of a radar system to extract information from a received echo. A behavioral model based on a Foster network topology has been developed to replicate the measured signal transients accurately. This model has been used to develop a digital predistortion technique that successfully counteracts the transients mitigating 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 performance metrics to quantify the effect of the transients on radar system performance and to test the effectiveness of a novel digital predistortion concept.