Multilevel security deals with the problem of controlling the flow of classified information. We present multilevel information flow control mechanisms for distributed systems that allow concurrent accesses to shared data. In a distributed computing environment, the different sites communicate through message passing. Our security mechanisms check the security of information flows caused by computations within individual sites as well as ones caused by communications among the sites. The correct behavior of the security mechanisms cannot be guaranteed if the allowed concurrency is left uncontrolled in the system. We present concurrency control mechanisms for the security mechanisms. In the presence of such concurrency control mechanisms, the consistency of the security data, which the security mechanisms rely upon, is preserved. Finally, we also present schemes to increase the efficiency and the precision of the security mechanisms.