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In this paper, the problem of blind separation of an instantaneous mixture of independent sources by exploiting their nonstationarity and/or nonGaussianity is addressed. We show that nonstationarity and nonGaussianity can be exploited by modeling the distribution of the sources using Gaussian mixture model. The maximum likelihood estimator is utilized in order to derive two novel source separation techniques. Both methods are based on estimation of the sensor distribution parameters via the expectation-maximization algorithm for GMM parameter estimation. In the first method, the separation matrix is estimated by applying simultaneous joint diagonalization of the estimated GMM covariance matrices. In the second proposed method the separation matrix is estimated by applying singular value decomposition of a weighted sum of the estimated GMM covariance matrices. The performance of the two proposed methods is evaluated and compared to existing blind source separation techniques. The results show the superior performance of the proposed methods in terms of interference-to-signal ratio.