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This paper addresses the problem of land-cover map updating by classification of multitemporal remote-sensing images in the context of domain adaptation (DA). The basic assumptions behind the proposed approach are twofold. The first one is that training data (ground reference information) are available for one of the considered multitemporal acquisitions (source domain) whereas they are not for the other (target domain). The second one is that multitemporal acquisitions (i.e., target and source domains) may be characterized by different sets of classes. Unlike other approaches available in the literature, the proposed DA Bayesian classifier based on maximum a posteriori decision rule (DA-MAP) automatically identifies whether there exist differences between the set of classes in the target and source domains and properly handles these differences in the updating process. The proposed method was tested in different scenarios of increasing complexity related to multitemporal image classification. Experimental results on medium-resolution and very high resolution multitemporal remote-sensing data sets confirm the effectiveness and the reliability of the proposed DA-MAP classifier.