In this paper it is explained how asteroids with large aphelion distances avoid very close approach to Jupiter. Namely, since for asteroids with resonant mean motions the critical arguments librate as it has been known for many years, and for those with non-resonant mean motions the eccentricities change with the argument of perihelion so the distance to Jupiter cannot be very small.

Also some behaviours of Kuiper-belt asteroids are studied by a similar way and it is found that the libration region for the argument of perihelion appears only when the eccentricity is very large. Therefore, even though the eccentricity is very large it is possible for any Kuiper-belt asteroid to avoid very close approach to any of the planets.