The target tracking system of an IR (InfraRed) guided missile is constantly subjected to disturbances due to the linear and angular motion of the missile. To diminish these LOS (Line Of Sight) disturbances the seeker of the missile can be built from a free gyroscope mounted in a very low friction suspension. The ability of the spinning gyroscope to maintain its direction relative to an inertial frame is used to stabilize the seeker LOS while tracking a target. The tracking velocity of the seeker, i.e. its angular velocity, is controlled by a feedback control unit where the signal from the IR detector is used as input. The electrical driven actuator consists of a set of coils and a magnet on the gyroscope. The purpose of this thesis is to develop a real-time model of the seeker gyroscope in an existing IR MANPAD (MAN Portable Air Defense) missile. The aim is a model that is able to simulate the real system with consideration to the tracking velocity. The model should also be integrated into a hybrid simulator environment. The final model is a grey-box model where the framework is based on physical modelling. Unknown parameters were determined using system identification methods.