A four-box model of the ocean–atmosphere is constructed that exhibits self-sustained oscillations in the regime of decadal to interdecadal periods found in oceanic general circulation models under certain boundary conditions. The oscillations are assumed to be caused by a type of baroclinic instability that relies on the store of available potential energy in the ocean. To represent this process in a low-order model, the authors propose Landau’s equation to govern the evolution of the overturning branch of the oceanic circulation. The domains of the unstable oscillations are found from linear stability analysis, and the nonlinear regimes are explored numerically. On these long timescales the atmospheric temperatures follow the oceanic temperatures. If the atmospheric temperatures are forced to be constant, the oscillations become strongly damped and disappear. The implications of the simple physics of this model for the decadal oscillations observed in more complex two- or three-dimensional GCMs are discussed.