Negative selection is a process from the biological immune system that can be applied to two-class (self and nonself) classification problems. Negative selection uses only one class (self) for training, which results in detectors for the other class (nonself). This paradigm is especially useful for problems in which only one class is available for training, such as network intrusion detection. Previous work has investigated hyper-rectangles and hyper-spheres as geometric detectors. This work proposes ellipsoids as geometric detectors. First, we establish a mathematical model for ellipsoids. We develop an algorithm to generate ellipsoids by training on only one class of data. Ellipsoid mutation operators, an objective function, and a convergence technique are described for the evolutionary algorithm that generates ellipsoid detectors.