This paper examines the CORBA Naming, Event, Notification, Trading, Time and Security Services, with the objective of identifying the issues that must be addressed in order make these Services fault-tolerant. The reliability considerations for each of these Services involves strategies for replicating the Service objects, and for keeping the states of the replicas consistent. Of particular interest are the sources of non-determinism in each of these Services, along with the means for addressing the non-deterministic behavior in the interests of ensuring strong fault tolerance.