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This paper deals with time-domain surface-impedance boundary conditions in computational magnetodynamics considering two dual finite-element formulations and a nonlinear magnetic constitutive law. Based on the resolution of the 1-D eddy-current problem in a semi-infinite slab, the massive conducting region is accounted for by choosing a number of exponentially decreasing trigonometric basis functions covering the relevant frequency range of the application in hand. Herein the method is elaborated for the magnetic-vector-potential formulation and the magnetic-field formulation. Results for both formulations are compared and validated on 2-D linear and nonlinear test cases.