The uptakes of gas-phase SO2 and H2O2 by ice surfaces have been investigated at temperatures from 213 to 238 K and from 10(-7) to 10(-4) Torr partial pressure. These experiments have been conducted in a low-temperature, coated-wall flow tube coupled to an electron-impact, quadrupole mass spectrometer which monitors changes in the SO2 and H2O2 partial pressure. The ice surfaces are formed by freezing liquid water. Unlike the uptakes of strong acids such as HNo3 and HCl, the SO2 and H2O2 uptakes are fully reversible on the time scale of the experiment and the surface coverages are roughly a thousandth of a monolayer at 10(-6) Torr partial pressure and 228 K. The SO2 uptakes scale with the square root of the partial pressure of the SO2 gas, indicating that dissociation of the hydrated form of adsorbed SO2 is occurring on the surface. The H2O2 uptakes scale linearly with the H2O2 partial pressure, indicating that dissociation does not occur. The uptakes are driven by H-bond interactions in this case. Support for these conclusions comes from uptake measurements with ice surfaces which were formed by freezing either acidic or basic aqueous solutions. Although the H2O2 uptakes are independent of pH, the acidic ice surfaces considerably inhibit the SO2 uptake and the basic surfaces enhance the SO2 uptake. The results in this paper are consistent with atmospheric observations which show that both S(IV) and H2O2 have low retention efficiencies after supercooled cloud droplets freeze, whereas the retention efficiency of HNO3 is high. The uptakes are sufficiently small that scavenging of SO2 and H2O2 by ice clouds will not be significant.