The system of differential motion equations of athe discrete-continuous model of a rotating elastic missile with a gas jet angular stabilization system is constructed for the motion perturbed by the transverse force pulse at missile leaving the guide line and side thrust component of the jet engine. Based on exact solution, transfer functions of the stabilization systems in the form of the ratio of quasipolynomials are obtained. The influence of the self-rotation velocity of the missile and the delay time in gas jet engines on the stability domains and the stabilization errors is studied.