The paper presents a design method of multivariable adaptive digital tracking PID controllers using genetic algorithms (GA) and its application to the attitude control and momentum management (ACMM) system for a space station. The controller comprises two parts : (i) a fast online recursive identifier using the least squares method with variable forgetting factors to provide the updated dynamic parameters of the plant; and (ii) a genetic tuner based on artificial genetic algorithms to tune online the parameter matrices of the controller. The application of the controller using GA to the ACMM system for the space station yields remarkable results in stability robustness and setpoint tracking behaviour with respect to the large moments of inertia variations.