A physically based parameterization for the nucleation and initial growth of ice crystals in cirrus clouds at low (<238K) temperatures prevailing in the upper troposphere and in the tropopause region is implemented in the ECHAM general circulation model. With that we performed the first interactive simulations of cirrus clouds in a global climate model. As homogeneous ice crystal nucleation requires relative humidities with respect to ice of 140 to 170% at these temperatures, we abandoned the saturation adjustment scheme previously used to compute the properties of cirrus clouds in GCMs. The comparison with relative humidity data taken on commercial aircraft showed that ECHAM reproduces the frequency distribution of supersaturation with respect to ice in cloud free regions well especially if high values of the subgrid scale vertical velocity are assumed. On the other hand, the higher frequency of occurrence of high supersaturations in the model may point to heterogeneous freezing as the missing mechanism for ice formation. In this talk we will show different sensitivity simulations of cirrus clouds formed by homogeneous freezing under normal conditions as compared to cirrus clouds formed shortly after the Mount Pinatubo eruption in 1991 to investigate if volcanic eruptions can affect cirrus clouds significantly.