The simultaneous spreading and evaporation of droplets of aqueous trisiloxane (superspreader) solutions onto a hydrophobic substrate has been studied both experimentally, using a video-microscopy technique, and theoretically. The experiments have been carried out over a wide range of surfactant concentration, temperature, and relative humidity. Similar to pure liquids, four different stages have been observed: the initial one corresponds to spreading until the contact angle, θ, reaches the value of the static advancing contact angle, θad. Duration of this stage is rather short, and the evaporation during this stage can be neglected. The evaporation is essential during the next three stages. The next stage after the spreading, which is referred to herein as the first stage, takes place at constant perimeter and ends when θ reaches the static receding contact angle, θr. During the next, second stage, the perimeter decreases at constant contact angle θ = θr for surfactant concentration above the critical wetting concentration (CWC). The static receding contact angle decreases during the second stage for concentrations below CWC because the concentration increases due to the evaporation. During the final stage both the perimeter and the contact angle decrease. In what follows, we consider only the longest stages I and II. The developed theory predicts universal curves for the contact angle dependency on time during the first stage, and for the droplet perimeter on time during the second stage. A very good agreement between theory and experimental data has been found for the first stage of evaporation, and for the second stage for concentrations above CWC; however, some deviations were found for concentrations below CWC.