Three different chemistry-climate models are compared with respect to their simulation of the stratospheric response to extreme cases of ENSO. Ensemble simulations of an unusually warm ENSO event (1940-1941) compared to a very cold event (1975-1976) reveal a weaker and warmer polar vortex in the Northern Hemisphere winter. This follows from anomalously propagating waves decelerating the zonal flow and strengthening the residual mean circulation. Models are in good agreement in simulating the observed (statistically reconstructed for the case 1941) flow in the lower stratosphere over the Pacific North American region, but less so over the North Atlantic European sector with insufficient reproduction of the wave structure. Modeled column ozone is reduced in the Tropics and increased on average in the northern extra tropics in accord with the general pattern seen in observations and in line with an intensification of the Brewer-Dobson circulation.