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In this paper, we assess and compare to observations the spatial characteristics of the twentieth Century ENSO SST variability simulated by 23 models of the IPCC-AR4/CMIP3 database. The analysis is confined to the SST anomalies along the equatorial Pacific and is based on the use of a non-linear neural classification algorithm, the Self-Organizing Maps. Systematic biases include a larger than observed proportion for modelled ENSO maximum variability occurring in the Western Pacific. No clear relationship is found between this bias and the characteristics of the modelled mean state bias in the equatorial Pacific. This bias is mainly related to a misrepresentation of both El Niño and La Niña termination phases for most of the models. In contrast, the onset phase is quite well simulated. Modelled El Niño and La Niña peak phases display an asymmetric bias. Whereas the main bias of the modelled El Niño peak is to exhibit a maximum in the western Pacific, the simulated La Niña bias mainly occurs in the central Pacific. In addition, some models are able to capture the observed El Niño peak characteristics while none of them realistically simulate La Niña peaks. It also arises that the models closest to the observations score unevenly in reproducing the different phases, preventing an accurate classification of the models quality to reproduce the overall ENSO-like variability. [ABSTRACT FROM AUTHOR]