In 2002 the external costs of air pollution from the Swedish transport sector were calculated using the methodology developed within the EU-funded ExternE-projects. A comparison of these estimates with those presently in use in Swedish transport analysis revealed important differences, especially for particulate matter. The main purpose of this project was to examine the calculations for Stockholm in the Swedish ExternE-study and based on the findings from this examination propose a method to be used for the cost calculation for pollutants with local impacts. In addition, the methods used for the cost calculation for pollutants with regional impact should be described. In the report, the results are presented in two parts. In the first part, the method we propose for the cost calculation for pollutants with local impact is presented. We suggest that the calculation is based on three components; exposure estimates, effects estimates and values. The product of these three gives the final cost. In this part of the report we also present the approaches currently used to calculate the cost for pollutants with a regional impact. In part two of the report we present in greater detail the findings from the examination of the calculations for Stockholm in the Swedish ExternE-study.