A mathematical model for the advancing contact-line motion on a smooth solid surface is proposed. It is shown that in the spreading of liquids over solid surfaces, the flow causes a surface tension gradient along the liquid-solid interface which influences the flow and, in the case of small capillary and Reynolds numbers, determines the dynamic contact angle and the force between the liquid and solid in the vicinity of the contact line. The model: (a) eliminates the shear-stress singularity of the classical model; (b) describes the fluid motion as rolling, in complete agreement with direct experimental observations; (c) determines the dynamic contact angle and the tangential force dependence on the contact-line speed; (d) explains the existence of the maximum contact angle values < 180°; (e) predicts a contact-line instability and an incipient air entrainment. It is shown also that, in the case of small capillary numbers, the force experienced by the solid in the vicinity of the contact line is determined by the surface tension gradient along the liquid-solid interface and not by the shear stress. A relationship between the parameters of Young's equation and the limiting dynamic contact angle value is found and a new method for independent measurement of these parameters is proposed. Qualitative and quantitative comparison of the theory with the experimental data of various authors is carried out. The model could be used in the treatment of a number of coating and multiphase problems with moving contact lines on smooth surfaces and gives a sound basis for conventional models developed for rough surfaces.