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This paper investigates the methods for learning predictive classifiers based on Bayesian belief networks (BN) - primarily unrestricted Bayesian networks and Bayesian multi-nets. We present our algorithms for learning these classifiers, and discuss how these methods address the overfitting problem and provide a natural method for feature subset selection. Using a set of standard classification problems, we empirically evaluate the performance of various BN-based classifiers. The results show that the proposed BN and Bayes multinet classifiers are competitive with (or superior to) the best known classifiers, based on both BN and other formalisms; and that the computational time for learning and using these classifiers is relatively small. These results argue that BN-based classifiers deserve more attention in the data mining community.