The power coupling coefficients between cores of waveguide systems with random geometrical imperfections along the fiber axis are determined by comparing numerical solutions of the coupled mode equations with numerical solutions of the coupled power equations and the dependence of the power coupling coefficient on the correlation length with respect to the propagation constants of modes is clarified. When the correlation length D is small the power coupling coefficient is proportional to κ 2 D where κ is the mean mode coupling coefficient and is independent of the fluctuation of the propagation constants. For sufficiently large D the power coupling coefficient dc decreases in proportion to D-1 with increasing D and when D , dc 0. Then the dependence of the power coupling coefficient on the mode coupling coefficient and the fluctuation of the propagation constants δ β is expressed as a function of a single variable κ /δ β .