We propose a new approach for dynamic control of redundant manipulators to deal with multiple prioritized tasks at the same time by utilizing null space projection techniques. The compliance control law is based on a new representation of the dynamics wherein specific null space velocity coordinates are introduced. These allow to efficiently exploit the kinematic redundancy according to the task hierarchy and lead to a dynamics formulation with block-diagonal inertia matrix. The compensation of velocity-dependent coupling terms between the tasks by an additional passive feedback action facilitates a stability analysis for the complete hierarchy based on semi-definite Lyapunov functions. No external forces have to be measured. Finally, the performance of the control approach is evaluated in experiments on a torque-controlled robot. (C) 2015 Elsevier Ltd. All rights reserved.