Anne Boutet de Monvel, Aleksey Kostenko, Dmitry Shepelsky, and Gerald Teschl Long-Time Asymptotics for the Camassa-Holm Equation (96K, LaTeX2e) ABSTRACT. We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Camassa-Holm equation for decaying initial data, completing previous results by A. Boutet de Monvel and D. Shepelsky.