Shared clusters represent an excellent platform for the execution of parallel applications given their low price/performance ratio and the presence of cluster infrastructure in many organisations. The focus of recent research efforts are on parallelism management, transport and efficient access to resources, and making clusters easy to use. In this thesis, we examine reliable parallel computing on clusters. The aim of this research is to demonstrate the feasibility of developing an operating system facility providing transport fault tolerance using existing, enhanced and newly built operating system services for supporting parallel applications. In particular, we use existing process duplication and process migration services, and synthesise a group communications facility for use in a transparent checkpointing facility. This research is carried out using the methods of experimental computer science. To provide a foundation for the synthesis of the group communications and checkpointing facilities, we survey and review related work in both fields. For group communications, we examine the V Distributed System, the x-kernel and Psync, the ISIS Toolkit, and Horus. We identify a need for services that consider the placement of processes on computers in the cluster. For Checkpointing, we examine Manetho, KeyKOS, libckpt, and Diskless Checkpointing. We observe the use of remote computer memories for storing checkpoints, and the use of copy-on-write mechanisms to reduce the time to create a checkpoint of a process. We propose a group communications facility providing two sets of services: user-oriented services and system-oriented services. User-oriented services provide transparency and target application. System-oriented services supplement the user-oriented services for supporting other operating systems services and do not provide transparency. Additional flexibility is achieved by providing delivery and ordering semantics independently. An operating system facility providing transparent checkpointing is synthesised using coordinated checkpointing. To ensure a consistent set of checkpoints are generated by the facility, instead of blindly blocking the processes of a parallel application, only non-deterministic events are blocked. This allows the processes of the parallel application to continue execution during the checkpoint operation. Checkpoints are created by adapting process duplication mechanisms, and checkpoint data is transferred to remote computer memories and disk for storage using the mechanisms of process migration. The services of the group communications facility are used to coordinate the checkpoint operation, and to transport checkpoint data to remote computer memories and disk. Both the group communications facility and the checkpointing facility have been implemented in the GENESIS cluster operating system and provide proof-of-concept. GENESIS uses a microkernel and client-server based operating system architecture, and is demonstrated to provide an appropriate environment for the development of these facilities. We design a number of experiments to test the performance of both the group communications facility and checkpointing facility, and to provide proof-of-performance. We present our approach to testing, the challenges raised in testing the facilities, and how we overcome them. For group communications, we examine the performance of a number of delivery semantics. Good speed-ups are observed and system-oriented group communication services are shown to provide significant performance advantages over user-oriented semantics in the presence of packet loss. For checkpointing, we examine the scalability of the facility given different levels of resource usage and a variable number of computers. Low overheads are observed for checkpointing a parallel application. It is made clear by this research that the microkernel and client-server based cluster operating system provide an ideal environment for the development of a high performance group communications facility and a transparent checkpointing facility for generating a platform for reliable parallel computing on clusters.