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We provide a discussion of bounded rationality learning behind traditional learning mechanisms, i.e., Recursive Ordinary Least Squares and Bayesian Learning. These mechanisms lack for many reasons a behavioral interpretation and, following the Simon criticism, they appear to be ‘substantively rational’. In this paper, analyzing the Cagan model, we explore two learning mechanisms which appear to be more plausible from a behavioral point of view and somehow ‘procedurally rational’: Least Mean Squares learning for linear models and Back Propagation for Artificial Neural Networks. The two algorithms look for a minimum of the variance of the error forecasting by means of a steepest descent gradient procedure. The analysis of the Cagan model shows an interesting result: non-convergence of learning to the Rational Expectations Equilibrium is not due to the restriction to linear learning devices; also Back Propagation learning for Artificial Neural Networks may fail to converge to the Rational Expectations Equilibrium of the model.