We have compared in situ measurements near the leading-edges of wave-clouds observed during the SUCCESS experiment with numerical simulations. Observations of high supersaturations with respect to ice (>50%) near the leading edge of a very cold wave cloud (T<-60 ¿C) are approximately consistent with recent theoretical and laboratory studies suggesting that large supersaturations are required to homogeneously freeze sulfate aerosols. Also, the peak ice crystal number densities observed in this cloud (about 4 cm-3) are consistent with the number densities calculated in our model. In the warmer wave-cloud (T≃-37 ¿C) relatively large ice number densities were observed (20--40 cm-3). Our model calculations suggest that these large number densities are probably caused by activation of sulfate aerosols into liquid droplets followed by subsequent homogeneous freezing. If moderate numbers of effective heterogeneous freezing nuclei (0.5--1 cm-3) had been present in either of these clouds, then the number densities of ice crystals and the peak relative humidities should have been lower than the observed values. ¿ 1998 American Geophysical Union