The dynamic equation of some nonlinear relative rotation system with two masses has been established, which contains a kind of nonlinear sick-slip friction. Chaotic motion and the control effect of multi-delay feedbacks of the nonlinear relative rotation system under external excitation are investigated. When the system is in chaos under external excitation, the multi-time delay is applied to control the chaotic motion. The chaotic critical conditions of parameters about Smale commutation are given in terms of Melnikov theory, while the influence of multi-delay feedbacks on the system movement state and chaotic critical conditions is studied. The control impacts of multi-time delay parameters on chaotic motion are studied by phase diagram, Poincare map and power spectrum, separately.