This article presents research data of the kinetics of Saccharomyces cerevisiae yeasts aerobic cultivation without forced air supply to the cultivator. Oxygen penetrates into the culture medium through its free surface and spreads throughout the liquid volume only due to molecular diffusion. Culture medium mixing occurs with pop-up bubbles of carbon dioxide and thermal energy released by the cells during their development. The result of the research was a generalized mathematical model of the kinetics of the yeast cells development, composed of two special models - the growth of biomass and carbohydrate consumption. The combination of the two models was carried out by introducing the relative specific velocity o s γ γ /γ 1 = into the mathematical model. There are specific rates of biomass growth and carbohydrate consumption in this equation. The obtained generalized mathematical model allows us to take into account the effect on the biological process of the initial values of biomass concentrations in the inoculation and the initial concentration of carbohydrates in the culture fluid, and to predict its progress outside the boundaries of the experiment. Experimental studies have confirmed the validity of this approach to the search for mathematical models of the kinetics of the development of yeast cells.