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In this paper, we discuss the influence of multiple bottlenecks on the stability of active queue management (AQM) controllers, usually configured on a single bottleneck basis. To see this, we consider a network scenario where RED is configured at each router according to previously developed control theoretic techniques. These configuration rules assure stability in a single bottleneck scenario. Yet, we show that instability may arise when two links become congested. We justify this result through a multiple bottleneck model.