They're already thought to have nuclear weapons, a major difference to Iraq.
Q&A: Tackling North Korea's nuclear plans
The United States said in October 2002 that North Korea had admitted to having a programme to develop nuclear weapons. Publicly, North Korea has merely said it retains "the right" to have such weapons.
BBC defence correspondent Jonathan Marcus examines the background to Western policy towards the secretive regime in Pyongyang.
Q: What do we know about North Korea's nuclear weapons programme?
A: According to US accounts, the North Koreans admitted they had a nuclear weapons programme, along with a reference to "more powerful weapons" (assumed to be a reference to chemical or biological arms), at a meeting in October with Assistant Secretary of State James Kelly in Pyongyang.
The Bush Administration confronted the North Koreans with new evidence that showed that they had broken their agreement of 1994 to freeze all nuclear-related activities.
Most arms control experts suspect North Korea of pursuing an active weapons programme - certainly up to 1994 - but so far the necessary inspections by the IAEA (the International Atomic Energy Agency, the UN's nuclear watchdog) have been rejected by Pyongyang. The IAEA wants to sample fuel rods in a reactor cooling pond to try to work out if material has been diverted for a weapons programme.
Q: What is the possible size of the arsenal?
A: Very hard to say without the above inspections. Experts believe that North Korea may have extracted sufficient plutonium for a small number of bombs. The latest disclosures appear to relate to a parallel programme to enrich uranium with some technical help coming from Pakistan. Quite how far this has gone is not clear.
America's CIA said in November that North Korea also had the capacity to make more nuclear weapons than the one or two it is already believed to possess.
The CIA said spent fuel from a nuclear reactor shut down under the 1994 accord could be used to make between one and six more bombs.
Q: Should we be worried?
A: Yes - arms proliferation matters, especially when weapons of mass destruction fall into the hands of secretive, unpredictable regimes which may well be heading for catastrophic failure.
Many experts believe that the North Korean system is in terminal decline. Its people suffer great poverty and frequent famine. How the regime ends matters, and managing this potential crisis is made harder if it has nuclear arms.
There is also the danger that an unstable regime like this could provide such weaponry to third parties. North Korea already has a bad track-record in the proliferation of missile technology.
Q: Wasn't there a deal with the Americans to stop Pyongyang developing nuclear weapons?
A: Yes there was - the 1994 agreement - by which North Korea agreed to halt all its nuclear activities and in due course to allow full inspections of its materials and facilities. In return it was to be supplied with two power-generating reactors of a type that was less likely to prove a source of weapons-grade materials.
The reactors are being supplied by an international consortium known as Kedo with the bulk of the finance coming from South Korea and Japan.
Some early work has begun at the reactor site. But the programme is way behind schedule. And the Americans say that it is about time the North Koreans allowed inspectors in so that their work can be completed by the time critical reactor components are ready to be delivered.
The agreement was further thrown into doubt in November when Kedo decided to suspend heavy fuel oil shipments, which were due to tide North Korea over until the new reactors were finished.
Q: Why isn't George Bush threatening North Korea like Iraq?
A: Well, they are two rather different cases. North Korea is already an isolated regime with huge domestic problems. Two of America's regional allies - South Korea and Japan - have an active policy of engagement to try to win Pyongyang round to a more compliant line.
The US may believe that nuclear deterrence will stop North Korea from using its bomb. At the end of the day North Korea is believed to have the bomb, while Iraq does not yet have it. The view in the Bush Administration is that action has to be taken before a country gets a nuclear capability. With North Korea it is just too late, so Washington has to manage the consequences as best it can.
Q: Would North Korea have had help developing its nuclear arsenal?
A murky business. There have been all sorts of allegations about past Chinese help for example.
However, the Bush team now argues that more recently Pakistan has given North Korea critical help. This cooperation is said to have begun in the late 1990s and may well have continued even beyond 11 September last year.
The idea that one of America's key allies in the "war against terrorism" should be helping one of the "axis of evil" to develop nuclear arms presents a massive problem for the Bush foreign policy team.
Q: What can the international community do?
Caution, engagement, diplomacy seem to be the watchwords at the moment. The Americans are playing all of this down, clearly wanting to focus on one crisis at a time.
The US is likely to raise the whole question of North Korea's activities with China which is seen as one of the few outside powers with at least limited leverage over the secretive North Korean regime.
