The orbits of the five outer planets were computed by special perturbations over 120000 yr. There was revealed a remarkable libration of the orbit of Pluto relative to that of Neptune such that the distance be- tween the bodies is never less than 18 a.u. The mechanism of the libration is described. It is concluded that the orbit of Pluto is safe from very close approaches to Neptune and no particular instability results from the fact that the radius of perihelion of Pluto is less than the radius of the orbit of Neptune. The libration is characterized by an oscillation in the angle -2XN- P. The period of the oscillation is about 19 670 yr, the mean is about 180 , and the amplitude is about 760.