his oldest son, Kim Jung Nam, lives in macau, and was once rumored to be the successor but has since more or less fled the country.
his youngest son, Kim Jong-Un, is rumored to be the successor to the Kim dynasty, apparently he's "Just like his father" but who really knows what that actually means.
There was an incident a few months back in which Kim Jong-Un reportedly attempted to convince the Chinese government to either kill Kim Jong-Nam or have him turned over to North Korean authorities... but the elder brother, with his apparently strong connections with Chinese officials, was able to escape capture.
It's most likely Kim Jong-Un (or his father, I guess) attempted to silence Kim Jong-Nam because he could, at worst, challenge the regime and at best, provide foreigners a previously unfiltered view of the Kims and the political machinations of the DPRK. In the end however, the attempt backfired, and exposed a widening gulf between the Chinese government and the DPRK regime (since they were more willing to support Kim Jong-Nam than KJI/his successor).
Kim Jung-Il does have a middle son, Kim Jong-Chul, who is apparently so effeminate that he's been passed over for consideration as the successor, although as with most of his family and the North Korean elite you can expect him to have some sort of high level party/government position even if it's only symbolic.
KJI also has a daughter who's older than the 3 sons, Kim Sul-Song, who has served as his personal secretary for some time but is unlikely to succeed him (it's assumed this is because she's a woman and despite communism's perceived gender equality, korean tradition/confucianism puts a very solid glass ceiling in place)
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