This paper deals with the steady state spreading of slicks of oil continuously spilled on the surface of the water streaming. Laboratory experiments were performed in a recirculaing water channel by injecting the oil at various velocity ratios. In the experiments, variations of the width of oil slick in the downstream direction were measured. Theory is developed by means of the two-layered model which takes into account the lateral spread of oil slick whose spreading rate is assumed to be proportional to the advancing velocity of the one-dimensional density front in equilibrium state. Thus the governing equations of the meanthickness, mean velocity and the width of oil slick are derived. Calculated results of slick width show similar tendency with experimental data.