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An analysis of the performance of a synchronous digital communications system in which the clock rate of each station is established as the average of the clock rates of all incoming signals to each station is presented. Using both-end control, the system frequency is the average of the free-running frequencies of the phase locked oscillators, weighted by the number of inputs to each station. In single-end control, the frequency is a similar average plus a term, which is a function of changes in transmission path delay. Rules are derived defining how a transmision path delay change will be reflected in changes of total phase difference at each transmission path terminal. These phase changes reflect requirements for elastic storage of data at each transmission path termination. The dynamic stability of a simple two station network is analyzed mathematically. A subsequent technical paper  will report on the extensive analysis of the dynamic behavior of various system configurations using a computer simulation of the time history response to various perturbations.