When Gim Il-seong fell ill in the 90's, people also hoped that the nation would change under the son, Gim Jeong-Il. After Gim Il-seong died in 1994, people hoped that Gim Jeong-il would be incompetent, and the regime would fall apart (much like how people hope that Castro's Cuba reign would fall apart when he dies).
Fast forward 14 years, and North Korea's regime is still ongoing after the world's first hereditary Communist hand-over. The difference this time is that Gim Jeong-il has not named a successor as of yet. We knew that Gim Jeong-il would take over from his father, much like we know that Raul Castro would take over from his brother Fidel.
Gim Jeong-il has 3 sons. The eldest, Gim Jeong-nam, was thought to be the successor, but events may have lead up to the point where he is no longer considered the heir apparent. Gim Jeong-nam has been reported (everything denied by the North Korean government of course) covertly in Japan a few times. One time, he was actually caught with a forged Dominican Republic passport, and deported out of Japan. Other times, he has been reported to be seen with upscale escort girls in Japan.
He has also been reported to be living in Macau with his family for a few years until 2007, spending a lot of time gambling in the city's growing casino industry.
I've read that Gim Jeong-nam is back in the consideration as the successor, and who knows. Gim Jeong-il himself was supposedly quite the party boy before he himself became leader. It wasn't until Gim Jeong-il assumed leadership that he supposedly really settle down.
But, it's the second son, Gim Jeong-cheol (the eldest son of Gim Jeong-il's favorite wife) who is the rival heir. And he has the backing of North Korea's army.
