In this paper, the concept of task-priority for dynamically balanced two-wheeled mobile manipulator is addressed to deal with multiple tasks simultaneously. The body of two-wheeled platform, which is assumed to be one of the links of the manipulator, can only be controlled indirectly. This system requires active control to maintain its posture and balance due to underactuated structure, which makes the control of this system quite challenging. Since this system has many degrees of freedom, it is possible to perform variety of tasks at the same time. However, conflict between tasks may occur while performing multiple tasks simultaneously. In case of conflict, system should satisfy the balance constraint to avoid the dangerous situations. Using null-space projection based task-priority method ensures the fulfilment of balance at all cost and assigns lower priorities of the remaining tasks. Motion of the underactuated joint can be controlled not only by the wheel but also the actuated joint of the manipulator by proposed method. The validity of proposed method is illustrated by simulation results.