In this work, we present an automated method for the detection of cells nuclei boundaries in conventional PAP stained cervical smear images. The proposed method consists of three phases: a) the definition of candidate nuclei centroids set using mathematical morphology, b) the initial approximation of cells nuclei boundaries and c) the application of the Gradient Vector Flow (GVF) snakes for the final estimation of candidate cell nuclei boundaries. It must be noted that the initial approximation of each snake position is obtained automatically, without any observer interference. For the final determination of the nuclei in our images, we perform a fuzzy C-means clustering, using a data set of patterns based on the characteristics of the area enclosed by the final position of the GVF snakes. The proposed method is evaluated using cytological images of conventional PAP smears, which contain 3616 recognized squamous epithelial cells. The results show that the application of the GVF snakes entails in accurate nuclei boundaries, and consequently in the improvement of the performance of the clustering algorithm.