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Cervical cancer is a preventable disease and the dysplasia it causes can be scanned by using a pap smear test. It can be beneficial to develop a computer-assisted diagnosis system to make the pap smear test robust and widespread. The most fundamental part of such a system is the segmentation of nuclei and cytoplasm in cervical cell images. The aim of this study is to segment the nuclei in such images. First, markers on the nuclei are found by using mathematical morphology operations. Based on the obtained markers, marker-based watershed segmentation and balloon snake model are applied to find the nuclei contours in a data set consisting of cervical cell images. The data set is composed of six classes ranging according to the dysplasia degree of the cells. The results are evaluated according to the relative distance error measure, and the strengths and weakness of the methods are discussed.