In my thesis I examine the model reference adaptive control (MRAC) of a DC motor drive using digital simulation. In the first third of the paper, I present the MRAC method in general, and two basic methods of MRAC design process, the Lyapunov method and the MIT rule. With these two methods I deduce the mathematical model of MRAC, present a design process for first order systems, and examine the functioning of these systems with Simulink simulation software. In the second third of the paper I exmine an EZG-705.0 type, permanet magnet DC servo motor with a 4/4 chopper DC drive, with current and speed controller. First, I present a linear model of the DC motor and exmine the control of the DC chopper drive. After that I design a current controller. In the last third of this paper I design a PI-type speed controller, which serve as the comparation model for MRAC speed control. Using this PI speed controller and the Lyapunov method adaptive algorithm, an MRAC speed control will be designed for the DC motor model and the behavior of this controller will be compared with conventional PI speed control. In the last section I design an MRAC controller with MIT rule and compare with the previously designed controllers.