Hyperspectral imaging, which records a detailed spectrum of light arriving in each pixel, has many potential uses in remote sensing as well as other application areas. Practical applications will typically require real-time processing of large data volumes recorded by a hyperspectral imager. This paper investigates the use of graphics processing units (GPU) for such real-time processing. In particular, the paper studies a hyperspectral anomaly detection algorithm based on normal mixture modelling of the background spectral distribution, a computationally demanding task relevant to military target detection and numerous other applications. The algorithm parts are analysed with respect to complexity and potential for parallellization. The computationally dominating parts are implemented on an Nvidia GeForce 8800 GPU using the Compute Unified Device Architecture programming interface. GPU computing performance is compared to a multicore central processing unit implementation. Overall, the GPU implementation runs significantly faster, particularly for highly data-parallelizable and arithmetically intensive algorithm parts. For the parts related to covariance computation, the speed gain is less pronounced, probably due to a smaller ratio of arithmetic to memory access. Detection results on an actual data set demonstrate that the total speedup provided by the GPU is sufficient to enable realtime anomaly detection with normal mixture models even for an airborne hyperspectral imager with high spatial and spectral resolution.