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This paper is concerned with adaptive learning algorithms for Bayesian network classifiers in a prequential (on-line) learning scenario. In this scenario, new data is available over time. An efficient supervised learning algorithm must be able to improve its predictive accuracy by incorporating the incoming data, while optimizing the cost of updating. However, if the process is not strictly stationary, the target concept could change over time. Hence, the predictive model should be adapted quickly to these changes. The main contribution of this work is a proposal of an unified, adaptive prequential framework for supervised learning called AdPreqFr4SL, which attempts to handle the cost-performance trade-off and deal with concept drift. Starting with the simple Naïve Bayes, we scale up the complexity by gradually increasing the maximum number of allowable attribute dependencies, and then by searching for new dependences in the extended search space. Since updating the structure is a costly task, we use new data to primarily adapt the parameters. We adapt the structure only when is actually necessary. The method for handling concept drift is based on the Shewhart P-Chart. We experimentally prove the advantages of using the AdPreqFr4SL in comparison with its non-adaptive versions.