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Gaussian processes (GPs) represent a powerful and interesting theoretical framework for Bayesian classification. Despite having gained prominence in recent years, they remain an approach whose potentialities are not yet sufficiently known. In this paper, we propose a thorough investigation of the GP approach for classifying multisource and hyperspectral remote sensing images. To this end, we explore two analytical approximation methods for GP classification, namely, the Laplace and expectation-propagation methods, which are implemented with two different covariance functions, i.e., the squared exponential and neural-network covariance functions. Moreover, we analyze how the computational burden of GP classifiers (GPCs) can be drastically reduced without significant losses in terms of discrimination power through a fast sparse-approximation method like the informative vector machine. Experiments were designed aiming also at testing the sensitivity of GPCs to the number of training samples and to the curse of dimensionality. In general, the obtained classification results show clearly that the GPC can compete seriously with the state-of-the-art support vector machine classifier.