We utilize the GISS Global Climate Middle Atmosphere Model and eight different climate change experiments, many of them focused on stratospheric climate forcings, to assess the relative influence of tropospheric and stratospheric climate change on the extratropical circulation indices (Arctic Oscillation, AO; North Atlantic Oscillation, NAO). The experiments are run in two different ways: with variable sea surface temperatures (SSTs) to allow for a full tropospheric climate response, and with specified SSTs to minimize the tropospheric change. The results show that experiments with tropospheric warming or stratospheric cooling produce more positive AO/NAO indices. Experiments with tropospheric cooling or stratospheric warming produce a negative AO/NAO response. For the typical magnitudes of tropospheric and stratospheric climate changes, the tropospheric response dominates; results are strongest when the tropospheric and stratospheric influences are producing similar phase changes. Both regions produce their effect primarily by altering wave propagation and angular momentum transports, but planetary wave energy changes accompanying tropospheric climate change are also important. Stratospheric forcing has a larger impact on the NAO than on the AO, and the angular momentum transport changes associated with it peak in the upper troposphere, affecting all wavenumbers. Tropospheric climate changes influence both the AO and NAO with effects that extend throughout the troposphere. For both forcings there is often vertical consistency in the sign of the momentum transport changes, obscuring the difference between direct and indirect mechanisms for influencing the surface circulation.