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This paper presents different analytical and numerical approaches devoted to the analysis and design of axial eddy-current couplers. The main part of the work regards a pure analytical procedure based on variable separation method (VSM). This methodology requires a preliminary linearization of the structure to reduce the three-dimensional (3-D) problem to a two-dimensional (2-D) one. The 2-D analytical model is compared with 2-D finite-element (FE) analysis and the comparison shows the reliability of the proposed model. The analytical procedure is then largely employed for a detailed parametric study to give useful information to the designer of eddy-current couplers. A double-sided stator with permanent magnets and single and multilayer conductive disk rotors are considered. In order to take into account 3-D effects, two different models are proposed. In the first one the VSM is coupled to a 2-D FE model; in a second model a closed analytical formula allows us to consider 3-D effects. All the models are validated with experimental results and with 3-D FE analysis.