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A new result is developed for separating nonlinearly mixed signals in which the nonlinearity is characterized by a class of strictly monotonic continuously differentiable functions. The structure of the blind inverse system is explicitly derived within the framework of maximum likelihood estimation and the system culminates to a special architecture of the 3-layer perceptron neural network where the parameters in the first layer are inversely related to the output layer. The proposed approach exploits both the structural and signal constraints to search for the solution and assumes that the cumulants of the source signals are known a priori. A novel statistical algorithm based on the hybridization of the generalized gradient algorithm and metropolis algorithm has been derived for training the proposed perceptron which results in improved performance in terms of accuracy and convergence speed. Simulations and real-life experiment have also been conducted to verify the efficacy of the proposed scheme in separating the nonlinearly mixed signals.