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Unsupervised Bayes sequential learning procedures for classification and estimation are often useless in practice because of the amount of computation required. In this paper, a version of a two-class decision problem is considered, and a quasi-Bayes procedure is motivated and defined. The proposed procedure mimics closely the formal Bayes solution while involving only a minimal amount of computation. Convergence properties are established and some numerical illustrations provided. The approach compares favorably with other non-Bayesian learning procedures that have been proposed and can be extended to more general situations.