In this paper, the Lindel?f's equations of nonholonomic rotational relativistic systems are studied. First, the quasi-velocities of nonholonomic systems and the Hamilton's principle of rotational relativistic systems are introduced. Next, the Lindel?f's equations and their improvable expressions in terms of generalized coordinats and quasi-corrdinates are obtained by using Hamilton's principle. Finally, by means of inprovable Lindel?f's equations, the new form of Chaplygin's equations is derived and the transitional method from relativistic analytical mechanics of the rotational systems to general analytical mechanics is illustrated.