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The paper deals with the problem of scheduling the transmission of periodic processes in a distributed FieldBus system, defining the conditions guaranteeing correct transmission. The scheduling of periodic processes fixes the transmission times for each process in a table, whose length is equal to the Least Common Multiple (LCM) of all the periods. This involves great memorization problems when some periods are relatively prime. The authors identify the theoretical conditions which allow the length of the scheduling table to be drastically reduced, but still guarantee correct transmission. On the basis of the theoretical conditions given, the authors present a pre-run-time scheduling algorithm which determines a transmission sequence for each producing process within the desired scheduling interval. An on-line scheduling algorithm is also proposed to schedule new transmission requests which are made while the system is functioning. The reduction in the schedule length may increase the number of transmissions, thus reducing the effective bandwidth and increasing the communication overload. In order to make as complete an analysis as possible of the scheduling solution, the authors also present an analysis of both the computational complexity of the algorithms proposed and the communication overload introduced.