We have developed a new infinite‐order perturbation approach for treating strongly anisotropic magnets. This formalism is based on a canonical transformation of a given system into a new system with an effective two‐ion anisotropy which, for example, can be treated by conventional spin‐wave techniques. An expression for the spin‐wave energy for the general conical magnetic moment configuration with arbitrary single‐ion anisotropy has been derived using this formalism. It was found that an analysis of the transverse spin‐wave spectra can at most result in a determination of a renormalized exchange integral and two renormalized anisotropy constants. A comparison of the theoretical predictions of this formalism with experimentally determined spin‐wave spectra indicate that a substantial part of the large two‐ion anisotropy, which had been previously introduced to describe the spin‐wave spectra in the heavy rare earth series, actually resulted from the fitting procedure which was used and not from any physical source.