— In this paper, we present a solution to the general problem of flow control for both unicast and multicast IP networks. We formulate a convex optimization problem that can be analytically solved with a low complexity. We show that with the proper choice of parameters, our problem can be fine-tuned to reward multicast flows or to provide max-min fairness. Further, our formulation can be deployed in the form of a centralized, decentralized, or quasi-centralized flow control scheme. Utilizing the solution to our optimization problem, we propose flow control algorithms requiring very little or no per flow state information. Our proposed algorithms can be implemented by making use of a simple ECN marking scheme to convey minimum per link or per zone flow fairness information to the end nodes. We also show how our flow control results can be adopted in the context of layered media multicast applications.