This work is focused on the analysis of manipulators with both joint and link flexibility. Due to the different order of joint and link stiffness, the full-order nonlinear system can be decomposed into different time-scale subsystems, namely, slow subsystem, mid-speed subsystem, and fast subsystem. It is shown that when the link stiffness is much greater than joint stiffness 01- when the two kinds of stiffness are comparable the vibrations due to joint or link flexibility can be suppressed whatever the control effort is made. Therefore, a composite control law is proposed in the case where the joint stiffness is much greater than the link stiffness to eliminate the structural vibrations while the tracking objective is achieved.