Multicomponent homogeneous nucleation is considered in the case of dominant and trace species (with respect to embryo composition). The free energy of embryo formation for multicomponent homogeneous nucleation has been derived for systems with several dominant species, e.g., water+sulfuric acid and a number of trace substances. This treatment is based on a differential version of the capillarity approximation. It is considered that an embryo is formed due to the condensation of several different gaseous compounds containing water, sulfuric acid, nitric acid, organic compounds, etc. Henry's law is employed to describe the chemical potential of trace species in embryos. The case of the surface free energy influenced by amounts of trace species transferred into an embryo is considered. It was found that the free energy of embryo formation for multicomponent nucleation depends upon the ratios of the partial pressures of the trace species to the Henry's law constants of the species. The nucleation rate for a multicomponent system is found to be a product of the dominant species nucleation rate (e.g., binary or ternary nucleation rate) and the correction factor that is influenced by the trace species. It was shown that the multicomponent nucleation correction factor is likely to be in the range from 3 to 10(10). As an example of the approach developed, the formation of secondary atmospheric aerosols was considered as multicomponent homogeneous nucleation of water vapor, sulfuric acid, nitric acid, formic acid, and other hydrophilic compounds.