We propose a new continuum description of the dynamics of sandpile surfaces, which involves two populations of grains: immobile and rolling. The latter move down the slope with a constant mean velocity and a certain dispersion constant. We introduce a simple bilinear form for the interconversion processes of sticking (below the angle of repose) and dislodgment (for greater slopes). We find a spinodal angle, larger than the angle of repose, at which the surface of a tilted immobile sandpile first becomes unstable to an infinitesimal perturbation. The effect of noise on our dynamical equations is briefly outlined.