Several years ago Kim Jong Il’s eldest son, Kim Jong-nam, was believed to be the favorite to succeed him as the next leader of North Korea. However, his apparent drunkenness and an embarrassing incident in Japan have caused him to fall from favor. Now it looks like Kim’s half brother, Kim Jong-Chul, who was recently spotted at an Eric Clapton concert in Germany, may be the new favorite.
Of course there is no guarantee that the Kim dynasty will survive at all. There are rumors that Kim Jong Il is not respected by the military as his father was, and some generals tried to take power and execute him and his family in the 1990s. There have been other attempts to kill Kim also in recent years. Look at this article for a pretty good analysis of who might be the next “Dear Leader” of North Korea.