In this paper an analytic approach to deal with vector diffusion problems into hysteretic materials is presented. A first procedure attempts to find a solution to the nonlinear problem approximating the differential magnetic permeability tensor by a set of polynomials; the second method reduces the tensor nonlinear terms to equivalent optimized linear coefficients. Scalar hysteresis cycles are reported to better show how the methods work and a hypothetic anisotropy is chosen to carry out preliminary results and discussions for vector problems.