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In two dimensional problems with the current flow in only one direction, the magnetic field can be solved by computing a scalar potential or one component of the vector potential. The general formulation for three dimensional solutions, including nonlinearities, is more complex and requires all three components of the vector potential as well as a scalar potential for the description of the fields. It is the purpose of this paper to present a general systematic formulation at low frequencies in terms of potential functions for three dimensional numerical solutions of the nonlinear electro-magnetic field problems that include either nonlinear magnetic materials or nonlinear electric materials. Special cases of the magnetostatic as well as eddy-current problems are discussed.