We have observed shear-wave splitting with (tSH--tSV)/tSV up to 1.5%, on long-period records of multiply reflected S waves bottoming in the uppermost mantle beneath the Russian and Siberian platforms. The dispersion of Love and Rayleigh waves over these paths shows discrepancies of comparable or larger magnitude with respect to smooth, isotropic (SI) structures, consistent with a model of the uppermost mantle having significant apparent vertical anisotropy. Although the splitting and dispersion data can be fit by smooth, anisotropic (SA) models, we have investigated the apparent anistropy associated with fine-scale (''rough'') structure beneath stable Eurasia. We fit the data with a rough, isotropic (RI) model having an rms shear velocity fluctuation that varies from 14% in the uppermost mantle to zero at 400-km depth. These fluctuations are larger than the variation in isotropically averaged parameters expected for even a diverse assemblage of upper-mantle ultrabasic rocks, which we take to be evidence for some sort of intrinsic (local) anisotropy. ¿ American Geophysical Union 1988