This paper proposes a coupled sliding-surface method for the design of trajectory control of a flexible-link robot. First, a sliding surface, coupling the joint velocity with the link bending moment at the joint, is defined based on the energy dynamics of the flexible link. Then a new trajectory-tracking control scheme is designed based on the coupled sliding surface, and extended to an adaptive scheme to cope with parametric uncertainties, where the Lyapunov stability theorem is used as a mathematical design tool. The proposed control is a collocated control designed based on a distributed-parameter dynamic model and hence is free from the so-called spillover instability. Using only the joint actuator, the proposed control guarantees stability throughout the entire trajectory control and asymptotic stability at desired goal positions. The proposed control is a PID control for the rigid dynamics and a proportional control for the flexible dynamics, with feed-forward and dynamics compensation. As a result, the proposed control guarantees zero steady-state joint-tracking errors even in the presence of low-frequency disturbances due to unavoidable mechanical inaccuracies in application. The theoretical results have also been proven by experimental studies.