The paper addresses the problem of the on-line identification of Petri Nets (PNs) modeling Discrete Event Systems (DESs) that exhibit unobservable events. The identifier monitors the DES events and the corresponding available place markings. Assuming that the observable transition set, the place set and the corresponding PN structure are known, at each event occurrence an identification algorithm defines and solves some integer linear programming problems. We prove that the complete PN system describing both the observable and unobservable DES behavior is recursively identified. An example shows an application of the proposed technique.