Analog computer and theoretical results are presented to show the nonlinear stability of any steady-state propellant temperature and flow in a typical nuclear rocket engine. This assurance of stability encourages design of schemes in which the neutronics are not closely controlled, e.g., schemes involving only propellant flow control or on-off drum controllers. A detailed analog computer model was assembled and checked against experimental data. Step-by-step approximations were made to simplify the nuclear engine dynamic behavior. This process continued until a small number of equations were found that adequately described this behavior and were amenable to theoretical analysis. For locked control behavior described by simplified theoretical equations, very large transients are proven to be stable. For the general theoretical case, only preliminary results are now available, but computer results indicate equally stable behavior.