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Given a general n-dimensional bimodal Gaussian mixture, this paper shows how unknown parameters may be found by the method of moments. Three cases are considered-equal modal probabilities, known but not necessarily equal probabilities, and all parameters unknown. The solution involves sample moments no higher than fourth order. For Gaussian mixtures where the number of modes is unknown, fourth-order moments can be used to count them, provided all modes have the same covariance matrix, and their multiplicity is not greater than data dimensionality. Examples of mode-counting and the determination of bimodal parameters are included.