Abstract: This paper derives a set of equations for the orbit and self-rotation of a synchronous binary-star system from the set of equations for non-synchronous binary stars. The numerical solutions of the equations as derived are subsequently given by using a numerical method. The circularization time, and the numerical values of the orbital semi-major axis, eccentricity, and the rotational angular velocity together with other parameters at that time are calculated for the synchronous binary-star system EKCep. The paper finally makes certain colollaries about the evolutionary trends of the orbit and self-rotation of the system.