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The abilities of three models (Climate Forecast System version 2 [CFSv2], Canadian Coupled Climate Model version 3 [CanCM3] and Canadian Coupled Climate Model version 4 [CanCM4]) in the North American Multimodel Ensemble for the East Asian summer monsoon (EASM) forecast were evaluated with their 29‐year hindcast data (1982–2010). Many EASM features including monsoon precipitation centres, large‐scale monsoon circulations and monsoon onset and retreat are generally captured by the three models and their ensemble mean, and the multimodel ensemble has the best performance. Since the East Asian domain includes the tropical western North Pacific summer monsoon (WNPSM) and the subtropical continent monsoon, two well‐known monsoon indices, the WNPSM index (WNPSMI) and EASM index (EASMI), and their associated low‐level winds and precipitation anomalies are well forecasted by the models. However, the forecast performance generally decreases as the leads increase, and the performance of EASMI is not as good as that of WNPSMI. CFSv2 forecasts well at leads up to 6 months whereas the skill of CanCM3 (CanCM4) decreases rapidly when the lead increases to 2 months (3 months). The failure of CanCM3 is mainly attributed to the poor forecast of the relationship of EASMI with the El Niño‐Southern Oscillation and Northern Indian Ocean‐western North Pacific (WNP) sea surface temperature anomaly. However, the causes of the poor forecast of CanCM4 for EASMI require further investigation. Sources of the forecast error (FE), which is the difference between model and observation for monsoon precipitation, are more significant than those of the predictability error (PE), which originates from the initial condition error, indicating that model deficiency plays a dominant role in limiting the EASM precipitation forecast. However, the PE cannot be neglected over the tropical western Pacific in CFSv2, over the WNP in CanCM3 and over the Tibetan Plateau in CanCM4. As the lead time increases, the FE does not remarkably change whereas the PE decreases significantly.