At least there is one O'Neill whose views on the dollar are absolutely clear. Jim O'Neill, the chief currency economist of the US investment bank Goldman Sachs, says: "Sometimes it feels as if I have spent most of my adult life saying that the dollar will weaken."

In fact, it has been closer to two years - still a long time for a leading investment bank to be wrong on the world's largest currency. Last week's falls in the dollar, particularly against the euro, have therefore given Mr O'Neill hope that some sanity is returning to the foreign exchange markets. But if the slide accelerates, it will pose a challenge for another O'Neill - the US Treasury secretary Paul.

After a confusion of comments on the subject from Mr O'Neill and other members of the Bush administration, there are now signs that the Treasury is moving towards replacing the deliberate support for a strong dollar with the idea that the markets are the best judge of where it should be - buttressed with the claim that current economic fundamentals justify its strength. H o w far such a hands-off policy would survive if the US currency went into free fall is an open question.

The reasons why the dollar should weaken, at least against the euro, are well known. The currency is markedly higher than almost any plausible estimate of its fair value. Goldman Sachs estimates that the currency's medium-term equilibrium rate is about $1.17 against the euro, though it seems close to fair value against the yen.

The widening US current account deficit, supported for so long by voracious domestic consumption driven by rising asset prices, now looks vulnerable. The Beige Book - a collection of anecdotal evidence from the Federal Reserve's regional banks - recently suggested the weakness in manufacturing was beginning to spread throughout the economy. And recent downward revisions to US productivity growth have helped undermine the idea that a US economic miracle can justify a permanent, sharply higher level for the dollar.

This, after all, is how open-economy macro-economics is supposed to work. Economies with large trade deficits and where domestic demand has run ahead of supply should see their currencies slide to boost exports relative to domestic demand.

But saying the dollar ought to fall against the euro is not enough. Dollar bears have been disappointed before by slides in the currency that were quickly reversed. The dollar endured another long hot summer in 1999, with a similar rash of questions about the durability and meaning of the strong dollar policy, before it recovered of its own accord.

Such reversals have made analysts increasingly reluctant to call the turn in the dollar. The latest independent forecasts from banks and consultancies collected by Consensus Economics shows it strengthening against both euro and yen by November from its current position.

There are other reasons to be cautious. The US economy looks a lot shakier than it did in the spring, after the Federal Reserve cut interest rates so sharply. But as the Bank of England pointed out recently when it cut UK growth forecasts, although the US economy is the biggest risk to world growth, the eurozone economy has deteriorated at an even faster rate in the past two months. The deciding factor may well be the gap between outcomes and expectations for the US economy.

"At the beginning, everyone talked about the slowdown lasting six to eight months rather than two to three years," says Sassan Ghahramani, president of G7 markets at Medley Global Advisors in New York. "Hardly anyone is talking about a swift US recovery now."

Market participants say most of the dollar selling so far seems to be from hedge funds and short-term speculative players, but large fund managers are likely to join in if the dollar fails to recover soon.

Capital flow data are notoriously slow to be released and in any case are imperfectly correlated with exchange rate movements. But guesses in the market - such as Goldman Sachs' estimates of potential flows arising from mergers and acquisitions - suggest that flows may be turning against the US.

Of course, a generalised dollar fall would be more welcome in some parts of the world than others. A stronger euro is good news for the eurozone, allowing the European Central Bank to cut interest rates by removing the threat of imported inflation. The same cannot be said for Japan: the US economy may look weak but Japan's is weaker. Unlike the ECB, the Bank of Japan seems to have run out of ways in which it can or will loosen monetary policy, notwithstanding last week's announcement that it was tinkering with its balance sheet to try to get banks to lend again. The last thing it wants is a stronger yen tightening monetary conditions. Recent verbal warnings from Japanese politicians against yen strength are likely to turn into renewed market intervention if the dollar falls further.

This contrasts with the laisser faire policy taking shape in the Bush administration. In an interview with the Financial Times last month, Mr O'Neill gave a robust defence of the dollar's strength. "How do you know the dollar is too high? Compared to what? What is it you know that the market doesn't know?" he asked. "Show me your evidence."

At the time, this looked like a reiteration of the strong dollar policy. But as time goes on, it begins to look more like a plea that the level of the dollar should be determined by the markets, not by where policymakers want it to go. This could be a way of reconciling Mr O'Neill's continued use of the expression "strong dollar" with comments from President George W. Bush that the value of the currency is best determined by the markets.

In a CNBC television interview last week, Mr O'Neill said the policy on the dollar was unchanged, while studiously avoiding any comment on what that policy was.

"The administration's commitment to a market-determined day-to-day exchange rate is a clear alternative to feeding the perception that it can - or will - influence the exchange rate via the nuances of a 'dollar policy'," says Mickey Levy, chief economist of Bank of America.

"They favour economic fundamentals consistent with a strong dollar, but this does not imply a willingness to intervene either directly or verbally to boost the dollar or lower it."

This interpretation was backed by Mr O'Neill last week when he said he thought the dollar would remain strong because of continued US productivity growth.

As long as the dollar enters a gradual depreciation, allowing the trade balance to adjust and investors to reposition themselves smoothly, Mr O'Neill's hands-off policy may pay dividends. But in the face of an accelerating depreciation, the credibility of this strategy would be less clear. Implying that any level of the dollar supported by the market is acceptable could lead the currency into free fall, destabilising markets and threatening a severe loss of confidence among US consumers and companies.

Moreover, observers note that while Mr O'Neill may have softened the mantra that the dollar should be strong, he seems to have adopted a prediction that it will be strong. This approach has its own risks.

Confident predictions about currencies, in the face of evidence to the contrary, have been the undoing of more than one policymaker. Mr Ghahramani notes that the only time in the past two years that ECB policymakers have got the rise in the euro they wanted is when they went on holiday and stopped talking about it.

"If Paul O'Neill keeps on saying he is in favour of a strong dollar while it is going down, he may well find himself a victim of the Duisenberg syndrome," says Jim O'Neill. "He would be better off just keeping his mouth shut and enjoying it."

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