A theory of heterogeneous water nucleation on aerosol particles consisting of soluble and insoluble substances has been developed. The case of partially wettable spherical insoluble core is considered. The theory links interfacial free energies of the surfaces, size of an insoluble core and chemical characteristics of the soluble substances with the ability of the aerosols to form water droplets. It is shown that water nucleation on such aerosols is strongly influenced by insoluble substances. The theory is compared with Kohler＇s theory and major differences in equilibrium pressure of water vapour and nucleation rate were found. These differences are explained by the influence of the insoluble substances on the free energy of embryo formation.