Abstract: A review of the theoretical data accumulated for the last decade on the diffusion kinetics of the stage of homogeneous nucleation of liquid droplets and gas bubbles in multicomponent systems has been presented. In addition to the previously known results, the review contains new relations and discussions that represent the further development of own studies. Thermodynamic expressions that relate the composition of critical droplets and bubbles occurring at unstable equilibrium with metastable multicomponent systems to the sizes of new-phase particles and degrees of supersaturation in the systems have been discussed. The dynamics of the growth of individual multicomponent supercritical droplets and bubbles at the stage of nucleation has been described at arbitrary values of vapor supersaturation for droplets and gas solubility in solutions for bubbles. The kinetics of the nucleation stage has been considered for ensembles of droplets and bubbles within the framework of the mean-field description of supersaturations and the excluded-volume approach. A relation has been shown between the excluded-volume approach to the description of the nucleation stage and the Kolmogorov crystallization theory.