In this paper we present a control-theoretic approach to design stable rate-based Bow control for ATM ABR services. The flow control algorithm that we consider has the most simple form among all the queue-length-based flow control algorithms, and is referred to as first-order rate-based flow control (FRFC) since the corresponding closed loop can be modeled as a first-order retarded differential equation. We analyze the equilibrium and the asymptotic stability of the closed loop for the case of multiple connections with diverse round-trip delays. We also characterize the asymptotic decay rate at which the stable closed loop tends to the equilibrium. The decay rate is shown to be a concave function of control gain with its maximum being the inverse of round-trip delay. We also consider an open loop control in which the queue control threshold is dynamically adjusted according to the changes in the available bandwidth and the number of connections. This open loop control is shown to be necessary and effective to prevent the closed loop from converging to an undesirable equilibrium point. (C) 1998 Elsevier Science B.V. All rights reserved.