WASHINGTON — In the 16 years since he assumed his father’s role as North Korea’s sole leader, Kim Jong-il has been denounced by the United States as a vicious dictator who starves his people, runs gulags, sets off nuclear tests and orders attacks on South Korean ships.

But now the Obama administration is concerned that what comes next could be worse.

What is coming, they fear, is Mr. Kim’s third son, Kim Jong-un, who is thought to have been the moving force behind a new wave of aggressive actions by the North and appears to be in line to succeed his father.

On Thursday night, Secretary of Defense Robert M. Gates — who took an intense interest in North Korea during his many years as an intelligence officer and then the director of the C.I.A. — offered an on-the-record glimpse of the administration’s internal analysis, saying that the North’s provocative actions were indications that the dictator’s son “has to earn his stripes with the North Korean military.”

He voiced suspicions that it was the succession struggle — in which Kim Jong-il is helping to build the credentials of his son, who is either 27 or 28 — that could explain the attack on a South Korean frigate, the Cheonan, that killed 46 South Korean sailors in March. “My worry is that that’s behind a provocation like the sinking of the Cheonan,” Mr. Gates said during an appearance in San Francisco.