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This paper presents gradient-based methods for simultaneous blind separation of arbitrarily mixed source signals. We consider the regular case where the mixing matrix has full column rank as well as ill-conditioned cases. Two cost functions based on fourth-order cumulants are introduced to simultaneously separate all separable single sources and all inseparable mixtures. By minimizing the cost functions, two gradient-based methods are developed. Our algorithms derived from gradient-based methods are guaranteed to converge. Finally, simulation results show the effectiveness of our methods.