A nonlinear generalisation of Principal Component Analysis (PCA) is applied to the 500mb geopotential height field of the Northern Hemisphere extratropical atmosphere. It is found that the low-frequency variability of the mid-troposphere is characterized by three distinct quasi-stationary states. The states are described and compared to those obtained from applications of cluster analyses and linear PCA to the height field. Evidence is provided that modes obtained through PCA (notably the Arctic Oscillation (AO)) are not independent dynamical modes of variability of the Northern Hemisphere extratropics. Rather they arise as the optimal linear compromise between the preferred quasi-stationary states of the circulation. ¿ 2001 American Geophysical Union