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An analysis of a pair of exchange-coupled magnetic thin films is outlined. The previous formulation of Goto et al. ensures that the first variation of the magnetic free energy is zero. In the present paper, an expression for the second variation of the energy is presented. Evaluation of this expression determines the stability of solutions to the coupled-film equations derived by Goto et al. In this way, magnetization curves and critical field plots are obtained exactly (i.e., the equations are not approximated) for pairs of exchange-coupled magnetic thin films. These results enable evaluation of coupled films as nondestructive readout (NDRO) memory elements.