A long-term project, aiming at systematic search for variable stars in Galactic Open Clusters (OCs), was started at the Geneva Observatory in 2002. We have been observing regularly a sample of twenty-seven Galactic Open Clusters in the U, B, V Geneva filters (hereafter U, B, V). The goal is to identify and to study their variable stars, as well as the connection between the variable stars in a cluster and the cluster properties. We present the status of this work in progress, and show preliminary results for one of these clusters, IC 4651.