The dynamic motion of a spinning rocket of varying moments of inertia under the influence of a varying torque is analyzed. The varying moments of inertia result from the rapid expenditure of fuel. The varying torque is produced by a constant rocket thrust asymmetrically applied while the body center of gravity location varies as the fuel burns. Aerodynamic forces are assumed negligible. The analysis is performed through the direct application of Euler's equations, which have a special applicability to this type of problem. The resulting motion is described in terms of Euler angles and resembles the motion of an ordinary top with nonsteady precession. The motion is compared to that of a body of fixed moments of inertia caused by a torque of fixed magnitude. It is shown that the variable aspects of the general problem create important characteristics of the resulting motion.