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We study the problem of guaranteeing deadlines of synchronous messages with their deadlines no more than periods in an FDDI network. In order to guarantee the transmission of a synchronous message before its deadline, a precise knowledge of the worst-case situation for such transmission is required. This paper studies the worst-case scenario for transmission of a synchronous message in an FDDI network, in which the time elapsed between arrival of the message and completion of its transmission will reach its maximum (i.e., the longest possible interval). A few conditions under which the worst-case situation can happen are formally derived.