I propose a method of seismic traveltime tomography in azimuthally anisotropic media consisting of dipping transversely isotropic layers. The model used for velocities is elliptical with variable inclination of the axis of symmetry. When used with the double elliptic approximation, the method can be used to fit general transversely isotropic media. This method is a generalization of conventional tomographic inversion techniques where the interfaces of the model are allowed to change their positions and to be eliminated from the inversion as iterations proceed, which allows a better estimation of the remaining unknowns. Ray tracing is performed in anisotropic models. The technique is tested with cross-well synthetic and field data where both strong anisotropy and strong velocity contrasts are present.