A Lyapunov function is constructed based on the weighted sum of entropies for the case of two open channels in cascade,which is described by the Saint-Venant equations.A class of boundary feedback controllers is presented to guaran- tee the local closed-loop asymptotic stability in a neighborhood of the equilibrium point by means of the Lyapunov design ap- proach. A Lyapunov function is constructed based on the weighted sum of entropies for the case of two open channels in cascade, which is described by the Saint-Venant equations. A class of boundary feedback controllers is presented to guaran- tee the local closed-loop asymptotic stability in a neighborhood of the equilibrium point by means of the Lyapunov design ap- proach.