In a token-passing ring Local Area Network (LAN) each message accumulates phase jitter as it travels around the ring. Unlike typical digital transmission systems, which tend to have random data traffic, ring systems carrying computer-generated traffic may have long strings of repetitive-pattern data. This traffic produces a jitter amplitude which is a function of the message statistics and the transmission characteristics of the physical layer. For the system to be stable, this jitter must be controlled. This paper describes the repetitive-pattern jitter generation and accumulation process and gives a methodology for designing the physical layer components to accommodate it.