This paper studies conditions where messages endlessly circulate in a system of IEEE 1588-2008 clocks. The study is based on two independent analysis techniques. One uses a discrete event simulation environment for describing the operation of the best master clock (BMC) algorithm in IEEE 1588-2008. The second uses a model checking tool. We discuss several cases illustrating conditions under which circulating messages occur and the effectiveness of measures to squelch these messages. This paper demonstrates that one or more of the squelching mechanisms must be implemented.