The key step of a computer-assisted screening system that aims at early diagnosis of cervical cancer is the accurate segmentation of nuclei. In this paper, we propose a two-phase approach to nuclei segmentation/classification in Pap smear test images. The first phase consists of a nested hierarchical partition (segmentation) that uses spectral, shape information as well as the class information. The second phase aims at obtaining nucleus regions and cytoplasm areas by classifying the segments resulting from the first phase based on their spectral and shape features, and merging of adjacent regions belonging to the same class. The classification of the individual regions is obtained using a Support Vector Machine (SVM) classifier. The experimental results are compared with the manual results obtained by the pathologist experts and demonstrate the efficacy of the proposed method.