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A brain microstate is defined as a functional/physiological state of the brain during which specific neural computations are performed. It is characterized uniquely by a fixed spatial distribution of active neuronal generators with time varying intensity. Brain electrical activity is modeled as being composed of a time sequence of nonoverlapping microstates with variable duration. A precise mathematical formulation of the model for evoked potential recordings is presented, where the microstates are represented as normalized vectors constituted by scalp electric potentials due to the underlying generators. An algorithm is developed for estimating the microstates, based on a modified version of the classical k-means clustering method, in which cluster orientations are estimated, Consequently, each instantaneous multichannel evoked potential measurement is classified as belonging to some microstate, thus producing a natural segmentation of brain activity. Use is made of statistical image segmentation techniques for obtaining smooth continuous segments. Time varying intensities are estimated by projecting the measurements onto their corresponding microstates. A goodness of fit statistic for the model is presented. Finally, a method is introduced for estimating the number of microstates, based on nonparametric data-driven statistical resampling techniques.