This paper is concerned with nonlinear analysis for the propagation of Rayleigh surface waves on a homogeneous, elastic half-space of general anisotropy. We show how to derive an asymptotic equation for the displacement by applying the second-order elasticity theory. The evolution equation obtained is a nonlocal generalization of Burgers' equation, for which an explicit stability condition is exhibited. Finally, we investigate examples of interest, namely, isotropic materials, Ogden's materials, compressible Mooney-Rivlin materials, compressible neo-Hookean materials, Simpson-Spector materials, St Venant-Kirchhoff materials, and Hadamard-Green materials. © 2009 by the Massachusetts Institute of Technology.