The results of an unprecedented international effort involving 26 countries are reported. The EUROMET.RI(I)-K1 and EUROMET.RI(I)-K4 key comparisons were conducted with the goal of supporting the relevant calibration and measurement capabilities (CMC) planned for publication by the participant laboratories. The measured quantities were the air kerma (Kair) and the absorbed dose to water (Dw) in 60Co radiotherapy beams. The comparison was conducted by the pilot laboratory MKEH (Hungary), in a star-shaped arrangement from January 2005 to December 2008. The calibration coefficients of four transfer ionization chambers were measured using two electrometers. The largest deviation between any two calibration coefficients for the four chambers in terms of air kerma and absorbed dose to water was 2.7% and 3.3% respectively. An analysis of the participant uncertainty budgets enabled the calculation of degrees of equivalence (DoE), in terms of the deviations of the results and their associated uncertainties. As a result of this EUROMET project 813 comparison, the BIPM key comparison database (KCDB) will include eleven new Kair and fourteen new Dw DoE values of European secondary standard dosimetry laboratories (SSDLs), and the KCDB will be updated with the new DoE values of the other participant laboratories. The pair-wise degrees of equivalence of participants were also calculated. In addition to assessing calibration techniques and uncertainty calculations of the participants, these comparisons enabled the experimental determinations of NDw/NKair ratios in the 60Co gamma radiation beam for the four radiotherapy transfer chambers.Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCRI Section I, according to the provisions of the CIPM Mutual Recognition Arrangement (MRA).