A theory (Barricelli, 1972) developed for the interpretation of planetary axial rotations is here applied to an interpretation of the axial rotations of major asteroids. The interpretation is based on the assumption that also asteroids can have satellite-systems, which may influence the axial rotation of the respective primaries. The reason why smaller asteroids tend to have slower axial rotation than the major ones as an average is discussed. Predictions of the theory can be tested by space-craft exploration of asteroids.