An efficient method for calculating the nucleation rates of H2SO4-H2O aerosol droplets is developed using classical nucleation theory for a binary vapor system. The nucleation model is used to predict binary homogeneous and heterogeneous nucleation rates in the exhaust stream of a supersonic aircraft flying in the stratosphere. Calculations indicate that, assuming at least 0.01% of sulfur is emitted as H2SO4, the H2SO4-H2O particle formation rate is large enough to enhance the background sulfate aerosol concentration substantially. Heterogeneous nucleation, although somewhat slower, may convert a substantial fraction of the soot particles into acid aerosols (notwithstanding rapid water vapor condensation on the soot). Model results are compared with a balloon measurement taken in the aircraft exhaust plume in which the sulfuric acid aerosol concentration was greatly enhanced above the background. The observed aerosols consist of pure sulfuric acid-water solutions without a nucleating ＇＇core,＇＇ which is consistent with the prompt homogeneous binary sulfuric acid nucleation in the jet plume. Simulations do not support an alternative delayed mechanism that requires photooxidation of SO2 into H2SO4 followed by homogeneous nucleation in the humid air (like the formation of new sulfate aerosols in volcanic eruption clouds).