The elastic nonlinearity in Rayleigh waves is investigated theoretically. Studies have revealed that nonlinearity in Rayleigh waves involves nonlocal as well as local effects [Parker and Talbot, J. Elast. 15, 389 (1985)]. Finite amplitude effects on sound in fluids are entirely local, and the effects on different wavelets are therefore independent. In contrast, the effects of nonlocal Rayleigh wave nonlinearity on a given wavelet are influenced by the properties of the entire wave. A time-domain evolution equation for Rayleigh wave propagation on the surface of an isotropic solid reveals the existence of nonlocal nonlinearity [Zabolotskaya, J. Acoust. Soc. Am. 91, 2569–2575 (1992)]. In the present study, the nonlinear operator in the evolution equation is investigated numerically and analytically. Numerical results show the dependence of the nonlinearity on the global properties of the waveform. An explicit analytical expression derived for the nonlinear operator permits the local and nonlocal contributions to be easily distinguished. Local versus nonlocal effects on waveform distortion are discussed. [Work supported by the David and Lucile Packard Foundation and by ONR.]