In most models of trusted database systems, transactions are considered to be single-level subjects. As a consequence, users are denied the ability to execute some transactions which can be run on conventional (untrusted) database systems, namely those that perform functions that become inherently multilevel in the MLS environment. This paper introduces a notion of multilevel transaction and proceeds to an algorithm for their concurrent execution. The algorithm is proven to be correct in the sense that resulting schedules for executing the multilevel transactions is one-copy serializable.