This study considers the lean angle stability problems in steering controlled tilting vehicles. Despite the fact that the considered nonlinear nonminimum phase model ignores some dynamic characteristics of the real system (we ignore wheel sleeping and wheel inertia), yet it captures important properties of the vehicle dynamics. We establish a stabilizing control strategy for the lean angle of the vehicle. To eliminate impulse behavior (due to the appearance of the derivative of the steering angle) we propose using Lyapunov stability theory a continuous feedback loop for the steering input signal that ensures exponential stability of a desired lean angle. The process of stabilizing a desired lean angle does not imply trajectory tracking, however the current approach can be extended to yield further results regarding trajectory tracking for the complicated model of a two-wheeled vehicle system like bicycles and motorcycles.