This paper is devoted to the finite-time tracking problem for multi-agent systems, where the control inputs are required to be bounded and the velocities are not available for feedback. An effective framework through defining a class of coordinated saturation functions is introduced, under which both a one-order finite-time observer and a high-order finitetime observer are constructed. By applying the homogeneous theory for stability analysis, it is proven that all the states of the followers can converge to that of the leader in finite time. Numerical simulations are presented to demonstrate the effectiveness of our control protocols. ©2013 IEEE.