Physiological systems are inherently nonlinear and nonstationary. Traditional analysis techniques that assume linearity and stationarity in the data may miss subtle transitional dynamic characteristics of the signal. This dissertation seeks to develop novel analysis techniques that explore the nonlinear and nonstationary characteristics of physiological signals. Specifically, these algorithms will be used to discern and quantify differences in dynamics of the renal autoregulatory (RA) mechanisms from normotensive and hypertensive rats. This work is separated into four specific aims. The first aim seeks to distinguish if the higher degree of variability in renal blood flow in hypertensive rats is due to deterministic chaos (DC) or time-varying characteristics of renal autoregulation. The results show that the Lyapunov exponent, which is used to quantify the degree of DC, can give erroneous results when the analyzed system has time-varying dynamics. To overcome this limitation, an algorithm was developed to specifically detect switching dynamics in RA. The second aim seeks to detect intra- and inter-nephron coupling via the auto- and cross-bispectra. The results show that nonlinear interactions in the form of phase coupling are in general less pronounced in hypertensive animals. The third aim seeks to detect very low frequency oscillations (∼0.01 Hz) in the form of amplitude modulation of renal autoregulatory mechanisms. The results show that amplitude modulation is reduced in hypertensive animals and also animals anesthetized with Inactin. The fourth aim seeks to develop and test a blood pressure control system based on the proportional-integral design. The main impetus for this aim stems from the observation from the third aim that anesthetics exert a depressive effect on RA. Therefore, this aim seeks to develop a control system to induce step changes in blood pressure to determine the step response from the kidney. In summary, various algorithms developed in this dissertation work were able to show nonlinear and nonstationary characteristics in RA not seen or misinterpreted from previous time-invariant studies. The algorithms presented are general algorithms and therefore can be applied to other physiological systems.