Evidence for millennial climate variations have been found in proxy records for the Late Glacial Maximum (LGM)and the Holocene. The millennial events in the Holocene appear to be much weaker than those of the LGM and may have an entirely different pattern due to differences in the ocean circulation. Solar variations, changes in atmospheric carbon dioxide and variations in tidal forcing have been invoked as possible forcing mechanisms to explain these Holocene millennial variations, but the Holocene millennial climate variations may be a purely internal oscillation of the coupled ocean-atmosphere climate system. To investigate this possibility a 1400 year long climate record of a model developed by Manabe and coworkers has been analyzed. The stability and excellent agreement with climatology make this simulation ideal for understanding global air-sea interaction on very long time-scales. The emphasis in the analysis is on the links between variations in ocean circulation and atmospheric fields on time-scales greater than one century. The results illustrate a strong relationship between anomalous trade wind strength and the slowly varying heat content of the Equatorial Pacific thermocline. There is a strong anticorrelation in the coupled model between rainfall in the Indonesian region and sea surface temperatures in the Eastern Equatorial Pacific on centennial time scales. Long-term variations of ocean heat content in different basins have two components. One corresponds to a global rise and fall of ocean heat content. The second component consists of opposite trends in heat gain or loss in the Atlantic and Pacific Basins with no systematic relationship to variations in heat content in the Southern Ocean. The variations in heat content are consistent with either changes in strength of the thermohaline circulation or basin wide changes in air-sea interaction on very long time-scales.