One of the main phases in the development of a system for the classification of remote sensing images is the definition of an effective set of features to be given as input to the classifier. In particular, it is often useful to reduce the number of features available, while saving the possibility to discriminate among the different land-cover classes to be recognized. This paper addresses this topic with reference to applications that involve more than two land-cover classes (multiclass problems). Several criteria proposed in the remote sensing literature are considered and compared with one another and with the criterion presented by the authors. Such a criterion, unlike those usually adopted for multiclass problems, is related to an upper bound to the error probability of the Bayes classifier. As the objective of feature selection is generally to identify a reduced set of features that minimize the errors of the classifier, the aforementioned property is very important because it allows one to select features by taking into account their effects on classification errors. Experiments on two remote sensing datasets are described and discussed. These experiments confirm the effectiveness of the proposed criterion, which performs slightly better than all the others considered in the paper. In addition, the results obtained provide useful information about the behaviour of different classical criteria when applied in multiclass cases.