Waterdrops were suspended in vertical systems of N2, Ar, or He gas with relative humidities of 0, 50, and 100% to determine the effects of evaporation and isotopic exchange on the deuterium and oxygen-18 contents of the drops. Equilibrium fractionation was found to exist between a drop and vapor at its surface (even during rapid evaporation in zero humidity atmospheres), but a kinetic fractionation occurred during diffusive transport of the vapor species (H2O, HDO, and H218O) between the surface of the drop and the free atmosphere. In dry atmospheres the kinetic fractionation was given by (D/D')n, where D/D' is the ratio of diffusion coefficients of H2O and HDO or H216O and H218O in the the particular gas used. The exponent n was found to be in good agreement with the value obtained from studies of evaporation rates of falling drops by previous authors (n=0.58). In moist atmospheres the kinetic fractionation depended also on the relative humidity and isotopic composition of the atmospheric vapor. Exchange adjustment times for isotopic equilibration of drops with saturated atmospheres were measured and found to be in agreement with theoretical predictions. Applications of the results to the study of atmospheric processes and isotopic fractionation during evaporation of lakes are discussed.