We have used the classical theory of homogeneous nucleation to calculate the freezing rate of sulfuric acid solution aerosols under stratospheric conditions. The freezing of stratospheric aerosols would be important for the nucleation of nitric acid trihydrate particles in the Arctic and Antarctic stratospheres. In addition, the rate of heterogeneous chemical reactions on stratospheric aerosols may be very sensitive to their state. Our calculations indicate that homogeneous freezing nucleation of pure water ice in the stratospheric solution droplets would occur at temperatures below about 192 K. However, the physical properties of H2SO4 solution at such low temperatures are not well known, and it is possible that sulfuric acid aerosols will freeze out at temperatures ranging from about 180--195 K. We also show that the temperature at which the aerosols freeze is nearly independent of their size. ¿American Geophysical Union 1991