Because the ATM Forum does not standardize the ABR flow control algorithm that an ATM switch should run, some ATM networks are likely to contain switches that run different ABR flow control algorithms. Even if all the switches within a "cloud" of switches use the same algorithm, individual clouds (each with it own algorithm) will be interconnected by virtual circuits. Virtual circuits which traverse multiple clouds will therefore be controlled by two different flow control algorithms concurrently. We explore some of the ramifications of mixing different flow control algorithms in the same ATM network. We identify the rate mismatch problem, which arises when a nonbottleneck switch (that uses one algorithm) interferes with the control of the bottleneck switch (that uses another algorithm). We formulate a hypothesis that states the conditions that lead to the rate mismatch problem. These conditions identify a specific class of problematic topologies. We validate the hypothesis formally and prove that rate mismatch causes unfairness. Using four different algorithms, in combinations of two at a time, we illustrate the interoperability of ABR flow control algorithms.