The purpose of this study is to examine Authority-Power Structure and Group-Attractiveness from the viewpoint of strength in match; to clarify what makes athletic clubs strong and to get materials to reinforce the Theory of Productivity-Attractiveness with. The subjects were 3,010 members of 100 Rugby-Fotaball clubs from universities and colleges all over Japan.They were examined and checked by means of questionaire and the following conclusions were reached. 1. As far as Authority-Power Structure is concerned, the stronger the Rugby-Fotball clubs are, the more clubs are of the outsider control pattern and of the outsider including oligarchy pattern. On the contrary, the weaker the clubs are, the more clubs are of the outsider excluding oligarchy pattern and of the membership pattern. 2. The stronger the Rugby-Football clubs are, the more members participated in athletic clubs in their junior and senior highschool days: their participation was for a longer term, their clubs were strong and many of them were captains. Especially, in their senior highschool days,many from the Rugby-Football clubs must have been excellent players. 3. The Stronger the Rugby-Football clubs are, the more days are alloted to practicing and the more individual members show higher participation ratio. But, by bettering the system and method of practice, the days and the participation ratio could be a little less and lower. 4. Compared with about twenty years ago, the Rugby-Football club members today tend to show self-centered, individualistic way of thinking. 5. In order to strengthen the Rugby-Football clubs, the amount of practice matters, that is,in strained human relationship with excellent managers and coaches. 6. In the Rugby-Football clubs, too, strength of match and group attractiveness are closely related with each other. This affirms the Theory of Productivity-attractiveness. 7. The factors regulating the strength of the clubs were examined according to their Authority-Power Structure. Outsider Controlled Pattern: the attractiveness of the club's prestige is stronger than other factors. When people other than managers and coaches take leader-ship, the clubs become weaker. Outsider Including Oligarchy Pattern: the attractivenesss of the club's prestige is also stronger than other factors. Generally speaking, the captain's strong leadership with his performance function makes the club strong. Outsider Excluding Oligarchy Pattern: these data can not be clarified but if we presume to say, when the club is managed in the strained human relationship with the captain and the senior members at its top, the strengh of the club increases.