Kinetics of spreading of aqueous surfactant solution droplets over highly hydrophobic substrates proceeds in one slow stage at concentration of surfactants below some critical value and in two stages if the surfactant concentration above the critical value: the fast and relatively short first stage is followed by a slower second stage. It is shown that the kinetics of spreading at concentrations below critical and the second stage at concentrations above critical are determined by a slow surfactant molecules transfer on a bare hydrophobic substrate in front of the moving three phase contact line (autophilic phenomenon). The latter process results in an increase of the interfgacial tension of the hydrophobic solid surface in front and the spreading as a result. It is proven that in spite of that the latter process results in a decrease of the total free energy of the droplet and, hence, the adsorption of surfactants molecules on a bare hydrophobic substrate in front of the moving three phase contact line is a spontaneous process. The duration of the first stage of spreading in the case of the surfactant concentration above the critical correlates well with the duration of adsorption of surfactant molecules onto liquid-air interface.The latter allows assuming that the adsorption on the liquid-air interface is the driving mechanism of spreading during the first fast stage of spreading at surfactant concentrations above the critical. It is discussed why the first stage does not present 2 in the case of surfactant concentrations below the critical concentration in spite of the longest duration of adsorption in this case.