Replication is crucial to achieve high availability distributed systems. However, non-determinism introduces consistency problems between replicas. Transactions are very well suited to maintain consistency, and by integrating them with replication, support for non-deterministic execution in replicated environments can be achieved. This paper presents an approach where a passively replicated transaction manager is allowed to break replication transparency to abort orphan requests, thus handling non-determinism. A prototype implemented using existing open-source software, Jgroup/ARM and Jini, has been developed, and performance and failover tests have been executed. The results show that while this approach is possible, components specifically tuned for performance must be used to meet real-time requirements.