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This paper presents a novel technique for addressing domain adaptation (DA) problems with active learning (AL) in the classification of remote sensing images. DA models the important problem of adapting a supervised classifier trained on a given image (source domain) to the classification of another similar but not identical image (target domain) acquired on a different area. The main idea of the proposed approach is iteratively labeling and adding to the training set the minimum number of the most informative samples from the target domain, while removing the source-domain samples that do not fit with the distributions of the classes in the target domain. In this way, the classification system exploits already available information, i.e., the labeled samples of source domain, in order to minimize the number of target domain samples to be labeled, thus reducing the cost associated to the definition of the training set for the classification of the target domain. In addition, we define a convergence criterion that allows the technique to stop the iterative AL process on the target domain without relying on the availability of a test set for it. This is an important contribution, as in operational applications, it is not realistic to assume that a test set for the target domain is available. Experimental results obtained in the classification of very high resolution and hyperspectral images confirm the effectiveness of the proposed technique.