An accelerating ducted propeller system for propelling boats offers enhanced performance, having the front end of the nozzle disposed at a radial distance (H) between 0.045D and 0.082D from the inner radius of the nozzle, where D is the inner diameter of the nozzle. The front end of the chord of the axial profile of the nozzle has a larger radius than the rear end of the chord with respect to the axis of rotation of the propeller. The inner surface of the nozzle at the axial distance (J) of 0.025D from the rear end of the output edge of the nozzle is at a radial distance from the inner radius of the nozzle of more than 0.0040D and less than 0.0300D. The radial difference between the inner radius of the nozzle and the outer radius of the profile of the nozzle is less than 0.092D.