Observations of shear wave splitting in the northeastern U.S. Appalachians and in the foredeep of the Urals vary significantly with the back azimuth and incidence angle of the incoming phase. These variations suggest two or more layers within the upper mantle with different anisotropic properties. Synthetic seismograms for simple multilayered anisotropic structures show that shear wave splitting parameters tend to vary substantially with the direction of approach. Relying on a subset of back-azimuth and incidence angle may strongly bias the model inferred, especially if the observations are averaged. On the other hand, the azimuthal splitting pattern provides additional constraints on vertical or lateral variation of anisotropic properties in the Earth. Using a new error estimation technique for splitting, we find that individual measurements from broadband data have errors of the order of Δϕ=3¿--7¿ for the fast direction and 0.1--0.2 s for the delay of split shear waves. The azimuthal variation of splitting parameters is broadly consistent throughout the Appalachian terranes in the northeast United States, especially for two long-running stations in the northeast United States, HRV (Harvard, Massachusetts) and PAL (Palisades, New York). Observations can be separated into two distinct populations, with mean fast-axis azimuths of N60 ¿E¿4¿ and N119 ¿E¿2¿. Delay values within each population range from near zero to ~1 s. Azimuthal splitting variation for ARU (Arti, Russia) in the foredeep of Uralian mountains is characterized by sharp transitions between different groups of observations. Using synthetic seismograms in simple structures, we develop one-dimensional anisotropic models under stations HRV and ARU. The model for HRV includes two layers of anisotropic material under an isotropic crust, with fast-axis azimuths N53 ¿E and N115 ¿E for the bottom and the top layers, respectively. The model for the upper mantle under ARU includes a layer with a fast-axis at N50 ¿E atop a layer with fast axis azimuth N90 ¿E. Our modeling confirms the need for a layer of strong anisotropy with a slow axis of symmetry in the lower crust under ARU, reported by Levin and Park <1997a>. Our results suggest that both Urals and Appalachians possess a relict anisotropy in the tectosphere, associated with past continental collision and accretion, underlain by anisotropy with orientation similar to the local absolute plate motion, suggesting an asthenospheric component to the signal. ¿ 1999 American Geophysical Union