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The properties of finite dimensional nonlinear systems relative to the numerical formulations of a class of three-dimensional electromagnetic field problems are discussed. These structural properties increase confidence in the results of the numerical calculation, since problems arising from multiple or chaotic solutions are a priori excluded. Numerical procedures for the computation of transient and steady-state solutions are presented and applied. The error introduced by the finite-element discretization is estimated making use of the properties of the dual electric and magnetic formulations.