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Land-cover classification based on multi-temporal satellite images for scenarios where parts of the data are missing due to, for example, clouds, snow or sensor failure has received little attention in the remote-sensing literature. The goal of this article is to introduce support vector machine (SVM) methods capable of handling missing data in land-cover classification. The novelty of this article consists of combining the powerful SVM regularization framework with a recent statistical theory of missing data, resulting in a new method where an SVM is trained for each missing data pattern, and a given incomplete test vector is classified by selecting the corresponding SVM model. The SVM classifiers are evaluated on Landsat Enhanced Thematic Mapper Plus (ETM + ) images covering a scene of Norwegian mountain vegetation. The results show that the proposed SVM-based classifier improves the classification accuracy by 5–10% compared with single image classification. The proposed SVM classifier also outperforms recent non-parametric k-nearest neighbours (k-NN) and Parzen window density-based classifiers for incomplete data by about 3%. Moreover, since the resulting SVM classifier may easily be implemented using existing SVM libraries, we consider the new method to be an attractive choice for classification of incomplete data in remote sensing.