Resilient Packet Ring (RPR) is a new standard, designated IEEE standard number 802.17, for MAN and WAN dual ring topologies. RPR uses the buffer insertion principle as a basis for its medium access control protocol. In this paper, we analyze parts of the aggressive mode of the RPR fairness protocol. We look at a congested node, and utilize control systems theory to analyze the stability of the associated fairness algorithm. In particular, we discuss how the settings of the two important parameters ageCoef and lpCoef influence the stability of an RPR-network. At the end of the paper we present simulated scenarios in order to illustrate our results.