Consideration is given to the application of multiversion schedulers in multilevel secure database management systems (MLS/DBMSs). Transactions are vital for MLS/DBMSs because they provide transparency to concurrency and failure. Concurrent execution of transactions may lead to contention among subjects for access to data, which in MLS/DBMSs may lead to security problems. Multiversion schedulers reduce the contention for access to data by maintaining multiple versions. A description is given of the relation between schedules produced in MLS/DBMSs and those which are multiversion serializable. The authors also propose a secure multiversion scheduler. They show that the scheduling protocol gives correct schedules and is free of covert channels due to contention for access to data, i.e., the scheduler is data-conflict-secure.