We propose a set of control strategies for performing two arm manipulation with the goal of simplifying the task definition. In order to develop these strategies we propose a new representation, derived from the cooperative task-space, in the dual quaternion domain. The result is a compact and "singularity free" representation for two arm systems, named cooperative dual task-space. All the proposed control strategies share the same general scheme and are derived by using an analytical approach. Moreover, the mathematical treatment is given in a coherent and systematic fashion, and thus other strategies may be derived using the same argument. Experimental results show the effectiveness and usefulness of the cooperative dual task-space framework and the proposed control strategies.