Stochastic Adaptive Control Results and Simulations The theme of this monograph is the adaptive control of systems in a stochastic environment and more precisely the study of the tracking problem for ARMAX SISO stochastic systems with time invariant and time varying parameters. Results of simultaneous tracking and parameter identification are included. The author has aimed to (1) provide a reasonably self contained and up to date exposition of the tracking problem after having properly placed it amongst numerous ideas approaches and subproblems related to adaptive control (2) display computer simulation results and discuss their comparative behaviour (3) introduce a new approach to the stochastic adaptive control with promising results and (4) qualitatively discuss the adaptive control problem in the hope of improving our understanding of it stimulate the informed reader to come up with new ideas and attract newcomers to its study. The reader is assumed to have studied control systems at the graduate level and to have a reasonably good grasp of basic probability theory. Apart from its educational value to the adaptive control student it is hoped that the accumulation of scattered results and their computer simulation as well as an extensive reference section will attract the active researcher in this field