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Segmentation and tracking of cells in fluorescence microscopy image sequences is an important task in many biological studies into cell migration as well as intracellular dynamics. The growing size and complexity of biological image data sets precludes manual analysis, and calls for increasingly advanced automatic algorithms that are generic enough to be easily tunable to different applications, yet robust enough to deal with different cell types and strongly varying imaging conditions. Active-contour based algorithms have proven to be very suitable for this purpose but still suffer from several shortcomings that limit their segmentation accuracy and tracking robustness. In addition, these algorithms are generally rather computationally expensive. In this paper, we present an advanced level-set based multiple-cell segmentation and tracking algorithm, which implements seven modifications compared to earlier algorithms that considerably improve its performance. Preliminary experiments on three different time-lapse fluorescence microscopy images demonstrate the potential of the new algorithm.