The local behaviour of root loci around zeros and poles is investigated. This is done by relating the Newton diagrams which arise in the local analysis to the McMillan structure of the open-loop system, by means of what we shall call the McMillan polygon. This geometric construct serves to clarify the precise relationship between the McMillan structure, the principal structure, and the branching patterns of the root loci. In addition, several rules are obtained which are useful in the construction of the root loci of multivariable control systems.