Hardware clocks used in computers tend to drift away from the correct time. In a distributed computer system, each hardware clock drifts away from the correct time at a different rate. In or4er to synchronise the clocks of each computer to the same time, some form of adjustment must be made to each clock. Internal clock synchronisation, where clocks can be adjusted so that all computers are synchronised to the same time relative to each other, is sufficient for some applications. Other applications require, external clock synchronisation, clocks are synchronised to some external time standard, such as Coordinated Universal Time (UTC), as well as to each other. Synchronisation between computers in the network is important for certain applications such as global ordering of events occurring throughout the system. Clock synchronisation can be implemented using extra hardware devices or by software alone. Many algorithms proposed to synchronise the clocks in a distributed computer system. Most of the proposed algorithms are deterministic. Deterministic algorithms are based on message passing between nodes. They guarantee a maximum deviation between clocks of the nodes but this maximum deviation is limited by the maximum end-to-end message transmission delay which can be very large. Recently some probabilistic algorithms proposed. These algorithms are still based on message passing but cannot guarantee a maximum deviation between computers in the network. Instead they guarantee a maximum deviation with a certain probability of failure. Such algorithms are not bound by the same constraint as the deterministic algorithms and can achieve much closer synchronisation. In chapter 2 backround information on clock synchronisation and the methods that have been published so far, at the end of the chapter the aims and objectives of the project will be given. Chapter 3 describes discoveries that were made about the clock systems in the deparment. Chapter 4 gives information on the first of the two algorithms studied in this paper. Chapter 5 describes a new algorithm that has been implimented on the departmental suns. Chapter 6 describes further work that could carry on from this project. Chapter 7 gives the conclusions to the project.