This report discusses theoretically the problem of mutual interference occuring in connection with the propeller performance of the propeller and rudder. Generally speaking, the efficiency of the propeller is dertermind by the ratio of the power applied to drive it to the fluid energy lost in the proppeller wake, and, therefore, it is obvious that the propeller efficiency can be increased by reducing the lost energy. The Contra-rudder was devised especially for this purpose. In this report, emphasis is plased on the development of the theory of Contra-rudder, and, first, in the basis of the momentum theory, it explains the dynamical mechanism of the recovery with the rudder of the lost energy of the propeller, and inquiries are made into the possibilities of other methods for recovering such energy. Next, in order to quantitatively calculate the changes occuring in the propeller when the propeller behind which the rudder is provided is put in motion, the calculating farmulae as obtained by the vortex theory are shown. Lastly, it expounds the method of designing a Contra-rudder based on the theory thus established, and the condition of the propeller for the purpose of assouring the highest efficiency of the propeller system in the case a Contra-rudder is provided. The experimental confirmation of the theoretical results, as clarified in the present report and the actual instances of the propeller system being designed will be expounded in the forthcoming report on “Experimental Study”.