Abastract In this thesis, two new approaches for handling multiple tasks in redundant manipulators based on predefined allocated priorities are proposed. The first approach is an integrated scheme which employs null-space base vector for handling prioritized tasks. Clear task and null-space representation, better execution of the lower priority tasks, and intuitive formulation are its basic features. The second approach aims to improve the performance of all the prioritized tasks, especially during algorithmic singularities beside clear null-space dynamics representation. This approach can be considered as a modification and extension of the Reverse Priority (RP) algorithm in acceleration level. The commands related to each tasks are added to each other following reverse order of priorities and by suitable projectors. The projector definition is given using minimal representation of the null-space. Clear null-space dynamics in the proposed methods facilitate the stability analysis on the null-space. A detailed evaluation by means of computer simulation in various cases is reported. Tasks accomplishment using the proposed approaches is compared with the classic method. In addition, this thesis addresses the problem of executing multiple prioritized task for robot manipulators with compliant behavior in the remaining null space. A novel controller-observer is proposed to ensure accurate accomplishment of various tasks based on a predefined hierarchy using a new priority assignment approach. Force control, position control and orientation control are considered. Moreover, a compliant behavior is imposed in the null space to handle physical interaction without using joint torque measurements. This issue is critical when robots are employed for complex manipulation in unknown environments and in the presence of human. During the manipulation in the dynamic environments, different objects may collide with the robot body and disturb its manipulation. In these cases, the robot is expected to continue execution of the tasks, accurately. Meanwhile, the robot should be compliant to ensure the safety during the interaction. Asymptotic stability of the task space error and external torque estimation error during executing multiple tasks are shown. Moreover, multiple tracking tasks during physical interaction is considered in this thesis. Considering tracking task in any arbitrary level of hierarchy control is one of the issues considered in this work. By using the suggested control method, multiple tracking tasks are accomplished accurately based on the assigned priority. Asymptotic stability of the task space errors, the null-space velocity and the external interaction estimation error during accomplishing multiple tracking tasks are shown analytically. Hence, the proposed nonlinear controller-observer covers all the limitations in previous method in tracking tasks. The performance of the proposed control approaches is evaluated on a 7R light weight robot arm by several case studies. Keywords: - Force control -position tracking -orientation control - prioritized task -impedance control