A microphysical model of aerosol size spectra that includes hygroscopic growth is presented. In the presence of atmospheric humidity, an aerosol size spectrum of the Junge [1952] type transforms into a superposition of two equilibrium power law spectra with indices determined by the original Junge index and the fraction of soluble material contained in the aerosol. The aerosol size distributions are presented as explicit functions of relative humidity H for three different humidity regimes: (1) moderate humidity, (2) high humidity but subsaturation, and (3) interstitial cloud aerosol. On the basis of this model of aerosol hygroscopic growth, the Twomey [1959] cloud condensation nuclei (CCN) power law is then derived so that its coefficients are related to the aerosol microstructure and humidity dependence under subsaturation. This simple aerosol model can be used in cloud and climate models that do not treat explicitly CCN activation and for evaluation of aerosol optical properties. An application for aerosol optical properties is considered by Khvorostyanov and Curry [this issue].