Hyperspectral (HS) images hold both spatial and spectral information of an imaged scene. This allows one to take advantage of the distinct spectral signatures of materials to perform classification tasks. Since HS data are also typically very large and redundant, it is appealing to utilize compressive sensing (CS) techniques for HS acquisition. CS avoids the need for postacquisition digital compression, as the compression is inherently performed electrooptically during acquisition. We research the performance of deep learning classification applied directly on the compressive measurements. We show that by using a spectral CS technique we previously developed, it is possible to reduce the captured data by an order of magnitude without significant loss in the classification performance.