The Lighthill–Giles [Philos. Trans. R. Soc. London Ser. A252, 397 (1960); J. Plasma Phys.19, 201 (1978)] method is extended to evaluate the far field resulting from a moving radiating source in an anisotropic and dispersive medium, and the result thus obtained has a retardation interpretation. The radiation energy flux derived from theJ⋅Emethod, only after a modification resulting from anisotropy of the medium and a correction factor resulting from retardation, is found to be compatible with that directly calculated from the far field, provided interference may be neglected. While the interference, which arises from the mixed product of any two far‐field terms of different wave vectors, is demonstrated to be completely null in a uniaxial medium for a stationary source, it is shown to exist in a gyrotropic magnetoplasma and the total Poynting vector could be substantially nonradial in certain special cases.