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We present a method for real-time geocorrection of images from airborne pushbroom sensors using the hardware acceleration and parallel computing characteristics of modern graphics processing units. This allows very fast geocorrection without accuracy loss with respect to traditional direct methods, with very little computational load for the central processor. Our method is based on a projective texture technique originally developed for fast shadow rendering. By combining the image data with inertial navigation and positioning ancillary data, we correct the image to a digital terrain model (DTM) and produce a geocorrected and georeferenced image. The method works independently of the number of channels of the sensor. Results with an ultralight hyperspectral system show that the speed achieved with standard hardware for a 1-m grid DTM gives better than real-time performance. This allows in-flight inspection of the geocorrected image during acquisition, for more efficient coverage of large target areas. In regard to accuracy, differences with standard ray tracing direct geocorrection remained subpixel.