Optimal detection analyses have been used to determine the causes of past global warming, leading to the conclusion by the Third Assessment Report of the IPCC that "most of the observed warming over the last 50 years is likely to have been due to the increase in greenhouse gas concentrations". To date however, these analyses have not taken full account of uncertainty in the modelled patterns of climate response due to differences in basic model formulation. To address this current "perfect model" assumption, we extend the optimal detection method to include, simultaneously, output from more than one GCM by introducing inter-model variance as an extra uncertainty. Applying the new analysis to three climate models we find that the effects of both anthropogenic and natural factors are detected. We find that greenhouse gas forcing would very likely have resulted in greater warming than observed during the past half century if there had not been an offsetting cooling from aerosols and other forcings.