This paper investigates the distributed tracking control problem for a class of Euler-Lagrange multiagent systems when the agents can only measure the positions. In this case, the lack of the separation principle and the strong nonlinearity in unmeasurable states pose severe technical challenges to global output-feedback control design. To overcome these difficulties, a global nonsingular coordinate transformation matrix in the upper triangular form is first proposed such that the nonlinear dynamic model can be partially linearized with respect to the unmeasurable states. And, a new type of velocity observers is designed to estimate the unmeasurable velocities for each system. Then, based on the outputs of the velocity observers, we propose distributed control laws that enable the coordinated tracking control system to achieve uniform global exponential stability. Both theoretical analysis and numerical simulations are presented to validate the effectiveness of the proposed control scheme.