Having in mind applications to an integrated digital network, the operation of the more frequently considered mutual synchronization system of N geographically-separated oscillators is here esamined, having recourse to a schematization so general as to guarantee in practice agreement between the mathematical model and the physical system. The results obtained bring out its poor reliability thus pointing to the convenience of proposing other systems. Therefore, as a solution, a new mutual synchronization system is suggested whose greater reliability is the consequence of better use of the information available in each control center.