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Support Vector Machines (SVMs) are an established tool for pattern recognition. However, their application to real-time object detection (such as detection of objects in each frame of a video stream) is limited due to the relatively high computational cost. Speed is indeed crucial in such applications. Motivated by a practical problem (hand detection), we show how second-degree polynomial SVMs in their primal formulation, along with a recursive elimination of monomial features and a cascade architecture can lead to a fast and accurate classifier. For the considered hand detection problem we obtain a speed-up factor of 1600 with comparable classification performance with respect to a single, unreduced SVM.