Summary: An unbounded anisotropic solid has a single plane of material symmetry, and a semi-infinite anti-plane (mode III) crack extends at a subsonic constant speed in an arbitrary direction in that plane. The exact solution for steady motion gives a dynamic stress intensity factor on planes radiating from the moving crack edge that achieves an invariant value when the plane lies directly ahead of the crack edge. The possibility that this value is a local maximum arises only for crack planes associated with the maximum and minimum values of the shear wave speed. For such planes, increasing the degree of non-orthotropy is found to increase the disparity between the maximum and minimum speeds. Calculations for such planes, moreover, show that nonorthotropy can restrict the speeds for which extension stability arises on planes of maximum shear wave speed. On the other hand, it also enhances fracture energy dissipation rates, especially on planes of minimum shear wave speed.