Finite-difference traveltime methods are an efficient way to calculate first arrival times at every point in a complex heterogeneous isotropic model. We show that Van Trier and Symes' algorithm can be extended to include anisotropy by replacing the isotropic dispersion relation inherent in their method with an anisotropic one. Unfortunately, the upwind method they use is difficult to implement in the anisotropic case, because it requires high-accuracy solutions of derivatives of complex anisotropic dispersion relations. For our preliminary results we use instead an easy-to-implement fixed-grid finite-difference method. This method works well in homogeneous anisotropic models, but seems to have trouble in heterogeneous ones.