Neural network models are used to reveal the nonlinear winter atmospheric teleconnection patterns associated with the El Ni¿o-Southern Oscillation (ENSO) and with the Arctic Oscillation (AO) over the N. Hemisphere. The nonlinear teleconnections (for surface air temperature, precipitation, sea level pressure and 500 hPa geopotential height) are found to relate quadratically to the ENSO and AO indices. Relative to linear teleconnections, nonlinear teleconections appear to propagate perturbations farther, into regions where classical linear teleconnections are insignificant.