Community structure is a key property of complex networks. Many algorithms have been proposed to automatically detect communities in static networks but few studies have considered the detection and tracking of communities in an evolving network. Tracking the evolution of a given community over time requires a clustering algorithm that produces stable clusters. However, most community detection algorithms are very unstable and therefore unusable for evolving networks. In this paper, we apply the methodology proposed in [14] to detect what we call community cores in evolving networks. We show that cores are much more stable than ”classical” communities and that we can overcome the disadvantages of the stabilized methods.