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This report addresses the issue of providing software for reliable distributed systems. In particular, we examine how to program a system so that the software continues to work in the face of a variety of failures of parts of the system. The design presented uses the concept of transactions: collections of primitive actions that are indivisible. The indivisibility of transactions insures that consistent results are obtained even when requests are processed concurrently or failures occur during a request. Our design permits transactions to be nested. Nested transactions provide nested universes of synchronization and recovery from failures. The advantages of nested transactions over single-level transactions are that they provide concurrency control within transactions by serializing subtransactions appropriately, and that they permit parts of a transaction to fail without necessarily aborting the entire transaction. The method for implementing nested transactions described in this report is novel in that it uses locking for concurrency control. We present the necessary algorithms for locking, recovery, distributed commitment, and distributed deadlock detection for a nested transaction system. While the design has not been implemented, it has been simulated.