In his first and second reports, the author has publicly announced his study on the theoretical consideration and model experimental results, dealing with the performance of rudders in open water, with special emphasis on the effect of the angular velocity of steering, and he believes that, the general state and tendency of the open rudder have been made clearer. This third report accordingly treats theoretically the effect of the propeller race on the performance of rudders. From the results of theoretical calculation of the rudder performance, the following results have been obtained : 1. To estimate the rudder force in propeller race, the most important factor is the velocity increasing coefficient of the propeller race, succeeding to the advance speed of the rudder and the helm angle. And 7080% of the total energy of the accelerated water energized by the propeller operates effectively on the rudder. 2. The effect of the angle of incidence generated by the propeller, is of the minor importance as far as the rudder of the symmetrical section is concerned. 3. If the gap between the propeller and the rudder is changed in the range of 0.51.5 R, it has little influence upon the rudder force. (R : radius of the propeller)