The nuclear tests carried out by India and Pakistan in May 1998 made the world realise that nuclear weapons had not gone away and indeed that they were beginning to spread after a hopeful period of renunciation by former Soviet states after the end of the Cold War.
The current crisis over North Korea's nuclear ambitions, uncertainties about those of Iran and pressure in the United States for nuclear testing to be resumed add to what Dr Gary Samore of the International Institute of Strategic Studies (IISS) in London called "not a pretty picture."
Dr Mohamed ElBaradei, the Director-General of the International Atomic Energy Agency (IAEA), the UN's nuclear watchdog, said recently: "The nuclear arms control regime is being challenged and is clearly under stress."
In 2005, a conference is to be held to review the progress of the Nuclear Non-Proliferation Treaty (NPT), the bedrock of efforts to stop the spread of nuclear weapons.
The basic deal made by the NPT was that non-nuclear states should not develop nuclear weapons while nuclear states should eventually get rid of them. The first ambition is slipping and the second is not going to be achieved.
Russia retains a large nuclear arsenal
Some states - the ex-Soviet ones Ukraine, Belarus and Kazakhstan - did get rid of their nuclear arsenals, as did South Africa, but the remaining core nuclear states - the United States, Russia, China, Britain and France - have no intention of doing so.
The US and Russia have, though, agreed to reduce their deployed warheads to about 2000 each by 2012.
And some nuclear-capable countries - India, Pakistan and Israel - just refused to sign up anyway, so are not hindered by international agreements.
New arms race
So the prospects are for more proliferation, especially in South Asia, the Far East and possibly in the Middle East.
India and Pakistan survived a potential nuclear confrontation in 2002 and have just started repairing their relations. But it is obvious that neither is going to stop its nuclear weapons development or the missiles that go along with them.
India is strongly committed to its nuclear programme
Both are reckoned to have about 20 or more devices at present and this number is expected to grow over the next few years.
The aim of other countries now seems to be the management of this stand-off. There is no realistic hope of getting either India or Pakistan to give up.
China is an interested party as well, since the 1998 Indian tests were partly designed with China in mind. The Indian missile called Agni (Fire) is capable of reaching China.
China itself has embarked on a nuclear modernisation programme. At present it relies heavily on static rockets, which are very vulnerable, and it wants many more mobile units.
The most immediate problem elsewhere is North Korea. It announced in January 2003 that it was withdrawing from the NPT under which its nuclear reactors were under IAEA inspection.
So far, the United States has avoided threatening North Korea. IISS' Gary Samore said: "The US is in a quandary. There is no attractive military option, one with a low price tag. This is not Iraq."
Talks have been held with the help of China but the outcome remains unclear. Is the North ready to bargain away its nuclear plans in exchange for economic assistance and assurances as to its own security and is the United States ready for that?
North Korea is seen by some as part of a wider problem.
We will not permit the world's most dangerous regimes and terrorists to threaten us with the world's most destructive weapons
Extract, US National Strategy to Combat Weapons of Mass Destruction
Anthony Cordesman of the Center for Strategic and International Studies in Washington said: "North Korea is a symptom of a much broader disease which existing arms control efforts are doing little to cure."
Next on the problem list is Iran.
The main issue is why it is building a centrifuge system with which to separate Uranium 235 from uranium ore. Uranium 235 is the key material in starting a nuclear reaction, and its acquisition is the main problem facing states which want to go nuclear.
Under the NPT, Iran is allowed to enrich uranium as long as it is under IAEA auspices.
The head of the Iranian nuclear programme, Gholamreza Aghazadeh, has said that Iran is simply developing its ability to provide nuclear energy.
However, the United States is not convinced and a confrontation with Iran is possible at some stage.
Israel, itself the possessor of a nuclear arsenal of unknown size, is also watching closely and is quite capable of taking unilateral action if it feels threatened as the destruction of the Iraqi reactor in 1981 showed.
The new post-9/11 American foreign policy is quite specific in one of its aims.
A document entitled "National Strategy to Combat Weapons of Mass Destruction" stated: "We will not permit the world's most dangerous regimes and terrorists to threaten us with the world's most destructive weapons."
Cause for concern
After Iraq, this pledge should not be doubted. But achieving its aim is now the problem.
Washington intends being active on many fronts - stopping the export of vital materials and technology, taking diplomatic action and piling on economic pressure, even preparing military action.
Some right wing voices in Washington are calling for South Korea and Japan to be encouraged to go nuclear
But it is at the same time considering developing a new generation of "mini nukes" itself.
These are small nuclear bombs which could, for example, be used to attack hardened stores of chemical or biological weapons. A Congressional report has called for such bombs to be developed.
These might need testing and if the US broke the current moratorium on testing, so could others. An American anti-missile system could encourage others, especially China, to build more missiles to overwhelm it.
And there are some right-wing voices in Washington calling for South Korea and Japan to be encouraged to go nuclear if there is no solution to the problem of North Korea.
The 2005 conference will have much to worry about.