Abstract: TEMPO keeps the clocks of computers in a local network synchronized with an accuracy comparable to the resolution of each individual clock. In a loosely-coupled network the machines can only compute the differences between the times of their clocks. A new algorithm has been devised to perform this measurement; a protocol based on it can adjust the clocks by means of a new system call that has been added to the kernel of clocks by means of a new system call that has been added to the kernel of the Berkeley UNIX 4.2BSD operating system. Several experiments show that a total quasi ordering can be based on the unique network timing maintained by the service.