Spectral image classification uses the huge amount of information provided by spectral images to identify objects in the scene of interest. In this sense, spectral images typically contain redundant information that is removed in later processing stages. To overcome this drawback, compressive spectral imaging (CSI) has emerged as an alternative acquisition approach that captures the relevant information using a reduced number of measurements. Various methods that classify spectral images from compressive projections have been recently reported whose measurements are captured by non-adaptive, or adaptive schemes discarding any contextual information that may help to reduce the number of captured projections. In this paper, an adaptive compressive acquisition method for spectral image classification is proposed. In particular, we adaptively design coded aperture patterns for a dual-arm CSI acquisition architecture, where the first system obtains compressive multispectral projections and the second arm registers compressive hyperspectral snapshots. The proposed approach exploits the spatial contextual information captured by the multispectral arm to design the coding patterns such that subsequent snapshots acquire the scene's complementary information improving the classification performance. Results of extensive simulations are shown for two state-of-theart databases: Pavia University and Indian Pines. Furthermore, an experimental setup that performs the adaptive sensing was built to test the performance of the proposed approach on a real dataset. The proposed approach exhibits superior performance with respect to other methods that classify spectral images from compressive measurements.