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We derive three computationally-efficient algorithms for the multichannel blind deconvolution of arbitrary non-Gaussian source mixtures. Two of the algorithms are spatio-temporal extensions of previously-derived blind signal separation algorithms that combine kurtosis-based contrast function optimization with output whitening. We analyze the local stability properties of the algorithms to determine the constraints on the step sine parameters to allow the separation and deconvolution of arbitrary signal mixtures. These analyses and supporting simulations illustrate the abilities of the new algorithms to effectively deconvolve and separate mixtures of arbitrarily-distributed sources.