The results of the HASP program to determine the role played by the stratosphere in the world-wide distribution of radioactive fall-out from nuclear weapons tests are presented. The program has operated since the fall of 1957. The sampling network using U-2 aircraft collected 10/sup 8/ scf of air from 57 S to 71 N up to 70,000 ft. Ashcan data are used for upward extrapolation. IPC Paper 1478 of near 100% efficiency is used. Stratospheric ruatter sampled is in the 0.01- mu range. Stratospheric inventories of Sr/sup 90/ were calculated for the periods Nov. 1957 to Dec. 1958, Jan. to Aug 1959, and Sept. to Nov. 1959 to be, respectively, 0.95, 0.81, and 0.7 megacuries. Concentrations were greater in the Northern Hemisphere by a factor of 2 to 3 than in the Southern Hemisphere. The Sr/sup 90/ maximum cccurs in the equatorial regions around 90,000 ft and slopes down to around 70,000 ft in the polar regions. Little fractionation is noted in stratospheric debris. Cesium-137 to strontium90 ratios are 1.8 to 0.5. A semiempirical application of Gaussisn diffusion is described which suggests that hot clouds injected in the equatorial stratosphere spread in the North-South direction with mixing coefficients near 5more » x 10/sup 8/ cm/sup 2// sec. Vertical mixing is slower with coefficients of 4 x 10/sup 3/ and 2 x 10/sup 4/ cm/sup 2//sec suggested for tropical and polar regions, respectively. An Injection-Depletion model is offered which indicates that as much as 50% of the material Produced in 1-Mt ground-surface burst comes down in local fall-out. Removal from the stratosphere occurs at different rates, depending on altitude and latitude of injection and season of the year. Effective half-residence times of 5, 10, snd 20 months, respectively, for polar, lowequatorial and high- equatorial debris are suggested. Surface concentrations of Sr/sup 90/ are displayed as a function of latitude and time. The Northeru Hemisphere carries threefourths of the bunden. The maximum burden of Sr/sup 90/ is predicted to occur in 1961; however, concentrations in food have probably reached their maximum value. The radiation hazard from fall-out is summarized. Fall-out has increased the dose msn receives from the natural-radiation background by abcut 2%. (auth) « less