Object permanence, the ability to mentally represent and reason about objects that have disappeared from view, is a fundamental cognitive skill that has been extensively studied in human infants and terrestrial animals, but not in marine animals. A series of four experiments examined this ability in bottlenose dolphins (Tursiops truncatus). After being trained on a “find the object” game, dolphins were tested on visible and invisible displacement tasks, and transpositions. In Experiments 1 and 2, dolphins succeeded at visible displacements, but not at invisible displacements or transpositions. Experiment 3 showed that they were able to pass an invisible displacement task in which a person’s hand rather than a container was used as the displacement device. However, follow-up controls suggested they did so by learning local rules rather than via a true representation of the movement of hidden objects. Experiment 4 demonstrated that the dolphins did not rely on such local rules to pass visible displacement tasks. Thus, like many terrestrial animals, dolphins are able to succeed on visible displacement tasks, but seem unable to succeed on tasks requiring the tracking of hidden objects.