In this paper we investigate the performances of the EFCI-based (Explicit Forward Congestion Indication) and ER-based (Explicit Rate) algorithms for the rate-based flow control of the ABR (Available Bit Rate) traffic in an ATM network. We consider the case of two switches in tandem. We present several definitions of bottleneck, and provide conditions that determine whether the first, the second or both queues are bottleneck. We show that it is not necessarily the queue with the slowest transmission rate that is «responsible» for a bottleneck. We derive analytic formulas for the maximum queue length. We compare our results to those obtained by approximating a network by a simpler one, containing only the bottleneck switch. We show that the maximum queue lengths under the approximating approach may largely underestimate the ones obtained in the real network.