The accuracy of perturbation methods for traveltime computations in anisotropic media is investigated as a function of the medium deviation from isotropy. The traveltime perturbation equations are briefly reviewed and a method for the choice of the isotropic background is proposed. The perturbed traveltimes are then compared with results of exact ray tracing for four different anisotropic models with orthorhombic symmetry and increasing anisotropy. The accuracy of the perturbed traveltimes is very good for media with small perturbations and decreases rapidly for perturbations larger than 15%. ¿ American Geophysical Union 1993