Multilevel transactions have been proposed for multilevel secure databases; in contrast to most proposals, such transactions allow users to read and write across multiple security levels. The security requirement that no high level operation influence a low level operation often conflicts with the atomicity requirement of the standard transaction processing model. In particular, others have shown that no concurrency control algorithm based on the standard transaction processing model can guarantee both atomicity and security. This conflict motivates us to propose an alternative semantic-based transaction processing model for multilevel transactions. Our model uses the semantics of the application to analyze an application and reason about its behavior. Our notion of correctness is based on semantic correctness instead of serializability as in the standard transaction processing model. Semantic correctness ensures that database consistency is maintained, transactions output consistent data, and all partially executed transactions complete. We show how an example application can be analyzed to assure semantic correctness and how this analysis can be automated. We also propose a simple timestamp-based multiversion concurrency control algorithm for transaction processing on a kernelized architecture. The advantages of our model over the standard transaction processing model are that atomicity can be assessed, and for some applications ensured via off line analysis, more concurrency is achieved, lesser synchronization between security levels is required, and a larger class of multilevel transactions can be processed.