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This paper reports on a simulation study of the relative performances of the ATM ABR and UBR service categories in transporting TCP/IP flows through an ATM Network. The objective is two-fold: (i) to understand the interaction between the window - based end-to-end flowcontrol TCP and the rate based flowcontrol ABR which is restricted to the ATM part of the network, and (ii) to decide whether the greater complexity of ABR (than UBR) pays off in better performance of ABR (than UBR).The most important conclusion is that there does not seem to be strong evidence that for TCP/IP workloads the greater complexity of ABR pays off in better performance.