A discussion is given of a simple mathematical model of the carbon dioxide cycle in atmosphere-biosphere-sea, with special attention to the possibility of self-sustained oscillations and to the behaviour of the cycle when additional carbon dioxide is injected from an outer source. The discussion is confined to phenomena with characteristic times of the order of 10–103 years leaving out the long geologic periods as well as the purely annual periods. Some numerical computations are also carried out on the electronic computer BESK. The discussion and the computations show that self-sustained oscillations possibly appear due to the presence of the sea, and that they generally are favoured when there exist time-lags in the biosphere of the order of a few decades. The computations also indicate that additional carbon dioxide injected at a rate corresponding to the present combustion of fossil carbon does not change significantly the carbon dioxide concentration in the atmosphere, since most part of it will be stored in the biosphere. Thus, the present theory suggests that the increase of carbon dioxide indicated by recent measurements may represent part of a natural self-sustained oscillation and not necessarily be a response to an increased combustion of fossils.