Investigations of the atmospheric fallout of 7Be and 210Pb in many places around the globe indicate that there are seasonal variations on the depositional fluxes of these nuclides: high in winter in a few places, while in most places the high occurs in spring. However, these earlier studies did not address quantitatively the corresponding seasonal variations of the amount of precipitation during these periods. Data on the depositional fluxes of 7Be and 210Pb in Galveston, Texas, during the years 1989--1991 indicate that the seasonal variation is not uniform from year to year, and the amount of precipitation primarily controls the depositional fluxes. All the recently published data on the depositional fluxes of these radionuclides to data are synthesized. Also, the seasonal variations of the depositional fluxes of 7Be and 210Pb due to the variations in the amounts of precipitation during these seasons are discussed. This study clearly shows that the depositional fluxes of 7Be and 210Pb during fall were minimum, and most of the time the fallout maxima were confined to either spring and/or summer. Interseasonal variations of the depositional fluxes of these nuclides do not remain the same. The data presented in this paper in conjunction with earlier published data seem to indicate that the observed seasonal increase in the depositional fluxes of 7Be during spring is not due to the troposphere-stratosphere exchange of air masses during that season. The 7Be/210Pb activity ratio values remain the highest in summer and this is attributed to the increased rate of vertical transport of 7Be (from the upper troposphere to the middle and lower troposphere) and 210Pb (from the lower troposphere to upper troposphere) due to decreased stability of the troposphere during summer months. ¿ American Geophysical Union 1995