Asymptotic properties of the Greens function of an electromagnetic field in the far zone of biaxial anisotropic media are examined, based on ideas proposed by Lax and Nelson [Phys. Rev. B 4, 3694 (1971)]. The rather complicated structure of the wave surface and the ray surface, in particular the existence of their singular points, is taken into account. Starting from a detailed analysis of the wave-surface Gaussian curvature, we find the directions of Greens-function asymptotic behavior differing from the usual R-1 relationship. These directions are the directions along the biradials of a biaxial medium, and the infinite sets of directions defined by a wave vector directed along every one of the binormals. In the first case, the asymptotical form of the Greens function is proportional to R-1/2; in the second case, this asymptotical form is proportional to R-5/4. A smooth transition from the asymptotic form proportional to R-1/2 to the usual asymptotic form is analyzed. The possibility of an experimental observation of this unusual asymptotic behavior is discussed.