The predictability of the coupled ocean–atmosphere climate system on interannual to decadal timescales has been studied by means of ensemble forecast experiments with a global coupled ocean–atmosphere general circulation model. Over most parts of the globe the model’s predictability can be sufficiently explained by damped persistence as expected from the stochastic climate model concept with damping times of considerably less than a year. Nevertheless, the tropical Pacific and the North Atlantic Ocean exhibit oscillatory coupled ocean–atmosphere modes, which lead to longer predictability timescales. While the tropical mode shares many similarities with the observed ENSO phenomenon, the coupled mode within the North Atlantic region exhibits a typical period of about 30 yr and relies on an interaction of the oceanic thermohaline circulation and the atmospheric North Atlantic oscillation. The model’s ENSO-like oscillation is predictable up to one-third to one-half (2–3 yr) of the oscillation period both in the ocean and the atmosphere. The North Atlantic yields considerably longer predictability timescales (of the order of a decade) only for quantities describing the model’s thermohaline circulation. For surface quantities and atmospheric variables only marginal predictability (of the order of a year) was obtained. The predictability of the coupled signal at the surface is destroyed by the large amount of internally generated (weather) noise. This is illustrated by means of a simple conceptual model for coupled ocean–atmosphere variability and predictability.