Theoretical calculations are presented for homogeneous and heterogeneous freezing of sulfuric acid droplets under stratospheric conditions, based on classical nucleation theory. In contrast to previous results it is shown that a promiment candidate for freezing, sulfuric acid tetrahydrate (SAT-¿ H2SO≡4⋅4H2O), does not freeze homogeneously. The theoretical results limit the homogeneous freezing rate at 200 K to much less than 1 cm-3s-1, a value that may be estimated from bulk phase laboratory experiments. This suggests that the experimental value is likely to be a measure of heterogeneous, not homogeneous nucleation. Thus, under stratospheric conditions, freezing of SAT can only occur in the presence of suitable nuclei; however, even for heterogeneous nucleation experimental results impose strong constraints. Since a nitric acid trihydrate (NAT) embryo probably needs a solid body for nucleation, these results put an important constraint on the theory of NAT formation in polar stratospheric clouds. ¿American Geophysical Union 1994