Over the past decade, numerous observational and modeling studies indicate that pollutant sources from one region often degrade air quality over other continents. A survey of the scientific literature reveals a wide range of estimates for the role of hemispheric transport in contributing to regional air pollution, likely reflecting divergent methods applied to address various objectives of individual studies. This divergence has prompted the Task Force on Hemispheric Transport of Air Pollution (TF HTAP; see www.htap.org) to organize an international multi-model effort to quantify and estimate uncertainties in source-receptor relationships for ozone, aerosols, mercury, and persistent organic pollutants among four northern hemispheric regions. The main focus will be on the ozone simulations, in which anthropogenic NOx, NMVOC, and CO emissions were decreased by 20%, individually and all together, in each of the four source regions (North America, Europe, East Asia, South Asia). Under the coherent modeling framework adopted here, the range of estimates narrows substantially from that in the literature. The models indicate a sensitivity of surface ozone to the combined influence of foreign sources that can range from 10-70% of the sensitivity to domestic sources, depending on the region and the season. An additional simulation in which global atmospheric methane was reduced by 20% yields a ~1 ppbv decrease in surface ozone in all regions consistently across the models. These results are feeding into a 2007 TF HTAP report and should provide a scientific basis for air pollution managers who may be faced with the challenge that future air quality improvements attained via regulations on domestic emissions could be offset by rising emissions in other regions of the globe.