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As part of EPRI Project RP 1288-1 methods have been developed for applying finite element techniques in developing large generator equivalent circuit models. In earlier work, non-steady-state effects have been handled on a linearized basis, invoking the assumption of small signals. This paper describes more elaborate finite element techniques, which include magnetic non-linearities in non-steady-state calculations. The two methods compared are (a) the direct time-integration of the finite-element vector potential diffusion equation and (b) solution of the diffusion equation with phasor time dependence, assigning variable permeabilities in an iterative manner. Results of the two methods are compared using simple, slab geometry, but at flux density levels where gross non-linearities exist. These results are viewed as providinig cross-verification of the two procedures, and provide the basis for application of these techniques to generator analysis.