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The conditions necessary to determine the minimum distance to the far-field zone are obtained for a finite source, emitting waves within an anisotropic medium. Although this distance is well known for free-space applications, little information is available pertaining to the far-field distance in an anisotropic medium such as a magnetized plasma. In this paper it is shown that the free-space criteria are not applicable to anisotropic media and, in some instances, they fail dramatically. It is shown that the principal curvatures of the wave number surface are important in determining the far-field distance. In an anisotropic medium, the principal curvatures depend upon the wave normal or propagation angle of the wave. Thus, the far-field distance depends not only upon the wave-length or magnitude of k, but also upon the direction of k as well. This implies that the far-field distance is not a constant at a given wave frequency, but varies with the direction of the observer from the source. Furthermore, one or both of the principal curvatures can be zero in an anisotropic medium and for wave propagation associated with these points on the wave number surface, there is no solution to the wave equation which represents a wave-amplitude dependence of 1/r.