The paper considers the approach to a stable steady state of a thermodynamic system in which certain of the forces have fixed values. These fixed forces are supposed large, so that the steady state is far from equilibrium. The equations of the system are linearized near the steady state.It is shown that two matrices occurring in the linearized equations are symmetric and positive definite. A Lyapunov function exists for the system. When the steady state is near to equilibrium the Lyapunov function reduces to the rate of production of entropy, measured from its value at the steady state.