Previous analysis of single-channel current records has shown that both the opening and closing transitions of chemically activated ion channels are operated by fast and slow kinetic processes. The fast component in the kinetics of channel opening has been interpreted as the reopening of a channel that has just closed. The fast component in the kinetics of channel closure has many possible explanations and is therefore more difficult to interpret. We can gain insight into the closing process by asking whether the lifetimes of successive openings of an acetylcholine receptor channel are correlated in open-state lifetime. Five kinetic models of channel closure are considered. Two of these models predict uncorrelated open-state lifetimes, one predicts correlated open-state lifetimes, and for two others a range of behavior is possible. Acetylcholine receptor channel data from cultured rat muscle are analyzed to show that open-state lifetimes are correlated, eliminating two models of channel gating.