Atmospheric testing of nuclear weapons began in 1945 and largely ceased in 1963. This testing is the major cause of distribution of man-made radionuclides over the globe and constitutes a background that needs to be considered when effects of other sources are estimated. The main radionuclides of long term (after the first months) concern are generally assumed to be 137Cs and 90Sr. It has been known for a long time that the deposition density of 137Cs and 90Sr is approximately proportional to the amount of precipitation. But the use of this proportional relationship raised some questions such as (a) over how large area can it be assumed that the concentration in precipitation is the same at any given time; (b) how does this agree with the observed latitude dependency of deposition density and (c) are the any other parameters that could be of use in a simple model describing global fallout? These issues were amongst those taken up in the NKS-B EcoDoses activity. The preliminary results for 137Cs and 90Sr showed for each that the measured concentration had been similar at many European and N-American sites at any given time and that the change with time had been similar. These finding were followed up in a more thorough study in this (DepEstimates) activity. Global data (including the US EML and UK AERE data sets) from 1954 – 1976 for 90Sr and 137Cs were analysed testing how well different potential explanatory variables could describe the deposition density. The best fit was obtained by not assuming the traditional proportional relationship, but instead a non-linear power function. The predictions obtained using this new model may not be significantly different from those obtained using the traditional model, when using a limited data set such as from one country as a test in this report showed. But for larger data sets and understanding of underlying processes the new model should be an improvement.