Starting from the operational space and task prioritization framework, presented in [L. Sentis and O. Khatib, Task-oriented control of humanoid robots through prioritization, in Proc. IEEE-Robotics and Autonomous Systems/RSJ International Conf. Humanoid Robots, Santa Monica, CA, USA, November 2004.], this paper proposes an extension and improvement of this approach, to make it applicable to nonholonomic tasks and systems. For the tasks where inequality type conditions have to be fulfilled, such solutions are obtained to ensure as small as possible movements at the joints, while keeping the actuators' driving torques between saturation limits. Having in mind that a prerequisite for realization of any task by biped robot is the maintenance of its upright position, this issue is also in the focus of our study. Instead of keeping the zero-moment point (ZMP) at an exact position, dynamic balance was ensured by allowing the ZMP to be anywhere within the support area. Since the condition for ZMP position is relaxed a smaller number of joints are engaged in the task realization, which enables more tasks to be handled simultaneously. Simulations were performed, and the results proved the validity of the proposed approach. When disturbance was applied compensation behavior emerged.