Detailed description of time-dependent behavior of multicomponent droplets is a necessary step in understanding the aerosol processes in the Earth's atmosphere. New experimental techniques for tracking the changes in temperature and chemical composition of small droplets (Lemoine and Castanet, 2013) extend the requirements to the modern theory of droplet growth. Multicomponent diffusion growth or evaporation of a droplet, for which the influence of surface curvature on the equilibrium vapor pressure can be neglected, proceeds with gradual approach to the stationary values of the concentrations of components and temperature in the droplet (Mattila et. al., 1997). The theory for the early stage of condensation or evaporation of a droplet, when size, temperature and composition of a droplet change simultaneously and can affect each other, has not been elaborated yet. We present here a rigorous derivation of a new set of equations for the size, composition and temperature of a small multicompone