This work describes sequences of extended morphological transformations for filtering and classification of high-dimensional remotely sensed hyperspectral datasets. The proposed approaches are based on the generalization of concepts from mathematical morphology theory to multichannel imagery. A new vector organization scheme is described, and fundamental morphological vector operations are defined by extension. Extended morphological transformations, characterized by simultaneously considering the spatial and spectral information contained in hyperspectral datasets, are applied to agricultural and urban classification problems where efficacy in discriminating between subtly different ground covers is required. The methods are tested using real hyperspectral imagery collected by the National Aeronautics and Space Administration Jet Propulsion Laboratory Airborne Visible-Infrared Imaging Spectrometer and the German Aerospace Agency Digital Airborne Imaging Spectrometer (DAIS 7915). Experimental results reveal that, by designing morphological filtering methods that take into account the complementary nature of spatial and spectral information in a simultaneous manner, it is possible to alleviate the problems related to each of them when taken separately.