CFTR, the ABC protein defective in cystic fibrosis, functions as an anion channel. Once phosphorylated by protein kinase A, a CFTR channel is opened and closed by events at its two cytosolic nucleotide binding domains (NBDs). Formation of a head-to-tail NBD1/NBD2 heterodimer, by ATP binding in two interfacial composite sites between conserved Walker A and B motifs of one NBD and the ABC-specific signature sequence of the other, has been proposed to trigger channel opening. ATP hydrolysis at the only catalytically competent interfacial site is suggested to then destabilize the NBD dimer and prompt channel closure. But this gating mechanism, and how tightly CFTR channel opening and closing are coupled to its catalytic cycle, remains controversial. Here we determine the distributions of open burst durations of individual CFTR channels, and use maximum likelihood to evaluate fits to equilibrium and nonequilibrium mechanisms and estimate the rate constants that govern channel closure. We examine partially and fully phosphorylated wild-type CFTR channels, and two mutant CFTR channels, each bearing a deleterious mutation in one or other composite ATP binding site. We show that the wild-type CFTR channel gating cycle is essentially irreversible and tightly coupled to the ATPase cycle, and that this coupling is completely destroyed by the NBD2 Walker B mutation D1370N but only partially disrupted by the NBD1 Walker A mutation K464A.