In this paper, the rolling stability of a power-generating tumbleweed rover is investigated. The nonlinear equations of motion of the rover capture the nonholonomic nature of rolling without slipping, the external wind force, and energy dissipation due to rolling friction and power generation. To assess stability of the system as it rolls about a preferred axis of rotation, Lyapunov’s indirect method is employed. When the shell of the tumbleweed rover has a uniform mass distribution, Lyapunov’s indirect method predicts instability; when the inertia about a preferred axis of rotation is increased, Lyapunov’s indirect method predicts stability. Numerical simulation results of both the linearized and nonlinear equations of motion confirm both the instability and stability predictions of Lyapunov’s indirect method.