In this paper, the task-space cooperative tracking control problem of networked robotic manipulators without task-space velocity measurements is addressed. To overcome the problem without task-space velocity measurements, a novel task-space position observer is designed to update the estimated task-space position and to simultaneously provide the estimated task-space velocity, based on which an adaptive cooperative tracking controller without task-space velocity measurements is presented by introducing new estimated task-space reference velocity and acceleration. Furthermore, adaptive laws are provided to cope with uncertain kinematics and dynamics and rigorous stability analysis is given to show asymptotical convergence of the task-space tracking and synchronization errors in the presence of communication delays under strongly connected directed graphs. Simulation results are given to demonstrate the performance of the proposed approach.