A simpli!ed model of the hovercraft is used having three degrees of freedom and the control is considered as having two inputs. This paper addresses the control law problem by reformulating the problem in terms of a direct Lyapunov approach whose derivation is performed using the symbolic manipulation program Maple. The proposed solution for this controller design formulation uses the control law instead of inverse dynamics to determine the coordinate histories for the unspeci!ed axes, and represents a novel approach for the control of the underactuated system such that the control law could stabilize both the actuated and underactuated axes. Simulation of the model is carried out in the MATLAB/Simulink environment, bringing a new effective method to solve the control problem of the hovercraft, which is a dif!cult system to control because its movement is subjected to nonholonomic constraints.