Coral reefs have been affected by natural and anthropogenic disturbances. Coral cover has declined on many reefs, and macroalgae have increased on some. The existence of alternative stable states with high or low coral cover has been widely debated, but not clearly established. We evaluate the evidence for alternative stable states in benthic coral-reef dynamics in the Caribbean, Kenya and Great Barrier Reef (GBR), using stochastic semi-parametric models based on large numbers of time series of cover of hard corals, macroalgae and other components. Only the GBR showed a consistent short-term regional decline in coral cover. There was no evidence for regional increases in macroalgae. The equilibrium distributions of our models were close to recently observed distributions, and differed among regions. In all three regions, the equilibrium distributions were unimodal rather than bimodal, and thus did not suggest the existence of alternative stable states on a regional scale, under current conditions.