Deposition densities (Bq m(-2)) of all important dose-contributing radionuclides occurring in nuclear weapons testing fallout from tests conducted at Bikini and Enewetak Atolls (1946-1958) have been estimated on a test-specific basis for 32 atolls and separate reef islands of the Marshall Islands. A complete review of various historical and contemporary data, as well as meteorological analysis, was used to make judgments regarding which tests deposited fallout in the Marshall Islands and to estimate fallout deposition density. Our analysis suggested that only 20 of the 66 nuclear tests conducted in or near the Marshall Islands resulted in substantial fallout deposition on any of the 23 inhabited atolls. This analysis was confirmed by the fact that the sum of our estimates of 137Cs deposition from these 20 tests at each atoll is in good agreement with the total 137Cs deposited as estimated from contemporary soil sample analyses. The monitoring data and meteorological analyses were used to quantitatively estimate the deposition density of 63 activation and fission products for each nuclear test, plus the cumulative deposition of 239+240Pu at each atoll. Estimates of the degree of fractionation of fallout from each test at each atoll, as well as of the fallout transit times from the test sites to the atolls were used in this analysis. The estimates of radionuclide deposition density, fractionation, and transit times reported here are the most complete available anywhere and are suitable for estimations of both external and internal dose to representative persons as described in companion papers.