We propose to observe the Jupiter Satellites Europa, Callisto and Ganymede and the Saturn satellite Iapetus in order to search for atmospheric components. Recent Galileo observations (Kliore et al., Barth et al.) have shown that atmospheres exists at least on Europa and Ganymede and also suggest that similar processes, interactions of charged particle radiation with water ice, should be observable at Callisto as well. On all targets we expect some mixtures consisting of H2O, H, OH, O2, O, SO2 and O3. The observations will provide answers on the respective abundances and their mixing ratios.