This paper deals with control of parallel manipulators for very high acceleration tasks including two case studies. The first one is the case of non-redundant parallel manipulators, where we are interested in control of PAR2 robot for 2D pick-andplace trajectories following. The proposed control scheme in this case is a nonlinear dual mode adaptive controller complied with a high gain state observer for the estimation of joint velocities. The second case study concerns redundantly actuated parallel manipulators, where we are interested in control of R4 robot for tracking of 3D pick-and-place trajectories. The proposed solution in this case is a dual-space adpative controller. The proposed controllers have been implemented in real-time on the two prototypes, and their effectiveness has been demonstrated through the obtained experimental results.