In order to understand the development of stem cells into specialized mature cells it is necessary to study the growth of cells in culture. For this purpose it is very useful to have an efficient computerized cell tracking system. In this paper a prototype system for tracking neural stem cells in a sequence of images is described. In order to get reliable tracking results it is important to have good and robust segmentation of the cells. To achieve this we have implemented three levels of segmentation. The primary level, applied to all frames, is based on fuzzy threshold and watershed segmentation of a fuzzy gray weighted distance transformed image.The second level, applied to difficult frames where the first algorithm seems to have failed, is based on a fast geometric active contour model based on the level set algorithm. Finally, the automatic segmentation result on the crucial first frame can be interactively inspected and corrected. Visual inspection and correction can also be applied to other frames but this is generally not needed. For the tracking all cells are classified into inactive, active, dividing and clustered cells. Different algorithms are used to deal with the different cell categories. A special backtracking step is used to automatically correct for some common errors that appear in the initial forward tracking process.