This paper is concerned with avoidance manipulability of redundant manipulators for trajectory tracking and obstacle avoidance. Possibility of avoiding a collision with obstacles during tracking a desired hand trajectory is discussed with the proposed avoidance matrix, avoidance manipulability ellipsoid and avoidance manipulability measure, which are defined on each link constructing the manipulator except the top link. A necessary and sufficient condition that the intermediate link can avoid obstacles in a working space is indicated when a dimension of range space of the avoidance matrix coincides with the one of the working space of the manipulator. That means the avoidance manipulability ellipsoid is expanded in the whole working space. Relations of the ellipsoids and factors that influence the shape, namely, a posture of the manipulator, redundant degree, a serial position of the intermediate link from base, and priorities of the avoiding tasks, are also analyzed. Finally, we show analyzed results of avoidance possibility with the proposed avoidance manipulability by numerical examples.