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Spectral variability remains a challenging problem for target detection and classification in hyperspectral (HS) imagery. In this letter, we have applied the nonlinear support vector data description (SVDD) to perform full-pixel target detection. Using a pure target signature and a first-order Markov model, we have developed a novel pattern recognition algorithm to train an SVDD to characterize the target class. We have inserted target signatures into an urban HS scene with varying levels of spectral variability to explore the performance of the proposed SVDD target detector in different scenarios. The proposed approach makes no assumptions regarding the underlying distribution of the scene data as do traditional stochastic detectors such as the matched filter (MF). Detection results in the form of confusion matrices, and receiver-operating-characteristic curves demonstrate that the proposed SVDD-based algorithm is highly accurate and yields higher true positive rates and lower false positive rates than the MF.