In the paper we present a formal model of real-time database (RTDB) systems using Duration Calculus (DC). First, we give a formal specification of the correctness for the executions of transaction systems and the Two Phase Locking Concurrency Control Protocol (2PL-CCP). We also give a formal proof for the correctness of the 2PL-CCP using the DC proof system. Then, we present a formal description of the real-time database model by extending the model for untimed databases with state variables expressing temporal objects and with DC formulas to express their behavior. A formal description of correctness of the parallel executions of transaction systems in RTDBs is then given as the combination of the correctness for the untimed case and the time constraints for the transactions and their read data.