This thesis discusses replication of non-deterministic objects in distributed systems to achieve fault tolerance against crash failures. The objects replicated are the virtual nodes of a distributed application. Replication is viewed as an issue that is to be dealt with only during the configuration of a distributed application and that should not affect the development of the application. Hence, replication of virtual nodes should be transparent to the application. Like all measures to achieve fault tolerance, replication introduces redundancy in the system. Not surprisingly, the main difficulty is guaranteeing the consistency of all replicas such that they behave in the same way as if the object was not replicated (replication transparency). This is further complicated if active objects (like virtual nodes) are replicated, and these objects themselves can be clients of still further objects in the distributed application. The problems of replication of active non-deterministic objects are analyzed in the context of distributed Ada 95 applications. The ISO standard for Ada 95 defines a model for distributed execution based on remote procedure calls (RPC). Virtual nodes in Ada 95 use this as their sole communication paradigm, but they may contain tasks to execute activities concurrently, thus making the execution potentially non-deterministic due to implicit timing dependencies. Such non-determinism cannot be avoided by choosing deterministic tasking policies. I present two different approaches to maintain replica consistency despite this non-determinism. In a first approach, I consider the run-time support of Ada 95 as a black box (except for the part handling remote communications). This corresponds to a non-deterministic computation model. I show that replication of non-deterministic virtual nodes requires that remote procedure calls are implemented as nested transactions. Unfortunately, effects of failures are not local to the replicas of a virtual node: when a failure occurs, nested remote calls made to other virtual nodes must be undone. Also, using transactional semantics for RPCs necessitates a compromise regarding transparency: the application must identify global state for it cannot be determined reliably in an automatic way. Further study reveals that this approach cannot be implemented in a transparent way at all because the consistency criterion of Ada 95 (linearizability) is much weaker than that of transactions (serializability). An execution of remote procedure calls as transactions may thus lead to incompatibilities with the semantics of the programming language. If remotely called subprograms on a replicated virtual node perform partial operations, i.e., entry calls on global protected objects, deadlocks that cannot be broken can occur in certain cases. Such deadlocks do not occur when the virtual node is not replicated. The transactional semantics of RPCs must therefore be exposed to the application. A second approach is based on a piecewise deterministic computation model, i.e., the execution of a virtual node is seen as a sequence of deterministic state intervals. Whenever a non-deterministic event occurs, a new state interval is started. I study replica organization under this computation model (semi-active replication). In this model, all non-deterministic decisions are made on one distinguished replica (the leader), while all other replicas (the followers) are forced to follow the same sequence of non-deterministic events. I show that it suffices to synchronize the followers with the leader upon each observable event, i.e., when the leader sends a message to some other virtual node. It is not necessary to synchronize upon each and every non-deterministic event — which would incur a prohibitively high overhead. Non-deterministic events occurring on the leader between observable events are logged and sent to the followers just before the leader executes an observable event. Consequently, it is guaranteed that the followers will reach the same state as the leader, and thus the effects of failures remain mostly local to the replicas. A prototype implementation called RAPIDS (Replicated Ada Partitions In Distributed Systems) serves as a proof of concept for this second approach, demonstrating its feasibility. RAPIDS is an Ada 95 implementation of a replication manager for semi-active replication for the GNAT development system for Ada 95. It is entirely contained within the run-time support and hence largely transparent for the application.