Abstract
The original Hassani transforms were introduced in the works of Algerian physicist M.E. Hassani. Hassani's generalized (superluminal) kinematics appeared in the cohntext of generalization and development of Hassani's ideas. In the present paper, applying Theorem of non returning for universal kinematics, it is proven that Hassani's generalized kinematics with positive direction of time are certainly time irreversible. From the physical point of view the last result means that in any time-positive Hassani kinematics temporal paradoxes are impossible basically, that is there is not potential possibility to affect the own past by means of "traveling" and "jumping" between reference frames.
