Several recent papers suggesting that the electrical conductivity of the lower crust and upper mantle are anisotropic have been based upon magnetotelluric (MT) observations of 'phase splits', the NIT analogue of shear wave splitting. The emphasis on the phase rather than the amplitude-response results from the distorting effect of conductivity variations in the overlying crust. These variations distort the amplitude response from deeper levels and make inferences based on the amplitude difficult. At the long periods needed to probe the conductivity at upper-mantle depths, the NIT phase response, a tensor, is negligibly affected by small scale conductivity variations in the overlying crust. However, the MT phase response of a half-space with a uniform but anisotropic conductivity is independent of polarization direction and no phase split occurs. Using simple anisotropic layered models we demonstrate that a phase split is produced by the conductivity change at the interface between the isotropic and anisotropic layers; the maximum phase difference reflecting the conductivity contrast (gradient) between the principal conductivities of the anisotropic layer and the isotropic layer's conductivity. In the general case, where none of the principal axes of the anisotropic conductivity layer lie in the plane of the surface, the orientation at which the maximum phase difference occurs (i.e. the principal axis of the phase tensor) is determined by the horizontal projection of conductivity tensor's ellipsoid. In such cases the orientation of the maximum phase split will not be aligned parallel to any of the conductivity tensor's principal axes. MT phase splits are a consequence of spatial differences or gradients in conductivity, not the intrinsic bulk properties of the conductivity (tensor) itself and in this respect are fundamentally different from shear wave splitting. (c) 2006 Elsevier B.V. All rights reserved.