The mathematical model of an infrared (IR) tracking system is developed. The system considered has a gyro-stabilized IR optical eye with rotating optical chopper. The dynamical equations of the gyro-mass assembly are derived. The equations that describe the signal processing in the electronic section of the system are obtained.Thus, the transfer functions that relates the precessional motion of the gyro assembly to the location of the IR-spot relative to the gyro spin axis are established. A physical simulation of the invloved system is then presented. A digital controller is employed to control the operation of the simulated tracking loop. The control is achieved via the parallel interface bus (HP-IB). The chopping action of the,tyro rotating reticle is physically simulated by placing an enlarged reticle in the front ,of an oscilloscope screen. The oscilloscope inputs are adjusted such that the oscilloscope,Spot traces a circle with angular frequency given by the gyro spinning speed. The electrimic part of the tracking system is inserted in the simulation loop. This hardware-in the loop procedure ensures that the simulation results are very close to reality. Via this simulation setup it is possible to develop and design the critical components of the system. In addition, the performance of the designed system can be tested. Simulation results show that the steady state tracking errors and the behavior of the tracking loop in: the transient period are affected by the IR spot intensity and size in the reticle plane.