In this paper, new sets of desired objectives will be introduced for dual user systems. It will be shown that the existing set of objectives leads to eliminate the effect of dominance factor from the picture, while this is an important factor in dual user system. Consequently, in this paper, two sets of desired objective containing the dominance factor are presented, which can be used in variety of applications. Then, an adaptive control methodology is presented to satisfy the desired objectives in the presence of unknown communication delay. Towards this end, new desired impedance equations are introduced for each set of desired objectives. Subsequently, the adaptive impedance control strategy is applied which brings the closed-loop system in the form of the desired impedances. The stability of closed-loop system is investigated through passivity theory and it has been shown that the controller maintains system stability despite of the undesired effects of communication delays. The main feature of the controller is that it does not require a-priori information of delay. In fact, the controller uses delayed signals sent through the communication channels and consequently, there is no necessity to know the delay value. The performance of the proposed control methodology as well as the importance of the proposed sets is validated through experiments.