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The dyadic Green's functions of Maxwell's equations in anisotropic media are found by a perturbation technique. The solutions are in Taylor's series which may be summed in closed form in the case of uniaxial crystal media. When the medium is biaxial or gyrotropic, approximation by partial sum may be used. The approximate solutions give the near fields in elementary functions, Which may be used to solve integral equations arising from scattering and radiation problems.