We examine the effects on receiver functions of transverse anisotropy and of dipping isotropic boundaries. Splitting of the Moho Ps phase predicts the anisotropy from a postulated 10-km-thick layer of highly anisotropic crustal material only when other phases can be well isolated and when allowance is made for the rotation of the incident energy out of the plane of energy propagation expected for isotropic models. We examine azimuthal variations of the synthetic radial and transverse receiver functions. For both transversely anisotropic layers and dipping isotropic boundaries, radial receiver functions are symmetric and transverse receiver functions are antisymmetric about a given back azimuth (the horizontal projection of the axis of symmetry or the dip direction). Differences include the following: (1) Transverse energy from dipping boundaries arrives at the time of the initial P phase no matter at what depth the dipping boundaries occur, while transverse energy arrives at the time of the initial P phase for anisotropic material only when the anisotropy is at the surface. (2) Transversely anisotropic systems with horizontal symmetry axes have waveforms with 180¿ periodicity as a function of back azimuth, while dipping symmetry axes or dipping boundaries just have 360¿ periodicity. A consequence of the symmetry is that stacking the initial P and Ps phases from transverse receiver functions for back azimuths that are 180¿ apart tends to decrease the arrivals from shallowly dipping isotropic boundaries and doubles the arrivals from anisotropic layers with horizontal symmetry axes. We examine receiver functions for station SNZO in New Zealand, above a subducting plate dipping at 15¿ beneath the station. Opposite polarities of transverse receiver functions separated by 180¿ in back azimuth suggest that either dipping isotropic layers or dipping axes of symmetry of anisotropic layers are present. The 15¿ dip of the subduction zone is insufficient to explain the energy on the transverse receiver functions by the isotropic structures previously determined from refraction and earthquake travel time inversion. However, modifying the isotropic models for the region by anisotropy determined via shear wave splitting measurements and refraction studies, allows many of the features of both the radial and transverse receiver functions to be explained. A relatively highly anisotropic layer about 7 km thick at the base of the crust with an axis of symmetry dipping at 20¿--40¿ may be caused by metamorphosed oceanic crust. ¿ 1998 American Geophysical Union