On-line full body imitation with a humanoid robot standing on its own two feet requires simultaneously maintaining the balance and imitating the motion of the demonstrator. In this paper we present a method that allows real-time motion imitation while maintaining stability, based on prioritized task control. Additionally, we describe a method of modified prioritized kinematic control that constrains the imitated motion to preserve stability only when the robot would tip over, but does not alter the motions otherwise. In the paper we give detailed description of all the steps of the algorithm, essentially providing a tutorial on the implementation of kinematical stability control. We present the results on the child sized humanoid robot called Compliant Humanoid Platform or COMAN. Our implementation for the first time shows reactive, stable on-line motion imitation on a large humanoid robot.