New York's main contract, light sweet crude for June delivery, fell 43 cents to close at 76.37 dollars a barrel.

In London, Brent North Sea crude for June rose 37 cents to settle at 80.49 dollars a barrel.

Trading was volatile a day after the eurozone plan drove sharp stock market rallies worldwide in relief that Greece's sovereign debt crisis and looming crises in other eurozone countries would be managed.

Crude futures had also surged on Monday, gaining a hefty 1.69 dollars in New York.

But European and Asian equities markets went into sell mode Tuesday as investor optimism faded about the rescue plan offered by the European Union and the International Monetary Fund to protect the eurozone from debt crises.

On Wall Street, stocks wobbled in the final hour of choppy trade.

"Concerns grew that the bailout may be insufficient despite the hefty one-trillion-dollar price tag," said Lawrence Eagles of JPMorgan Chase.

Barclays Capital analyst Amrita Sen agreed.

"Despite the agreed EU package to bail out the debt-laden European countries, fears of sovereign risk in the region remain and sentiment remains cautious," Sen said.

Ellis Eckland, an independent analyst, noted the oil market "almost completely" followed the equity market.

"The number-one concern for all traders, the main driver for the equity market, the main driver for the commodity market is the European situation," he said.

Phil Flynn at PFGBEST pointed out that oil bulls must be disappointed that the New York market had failed to test near 80 dollars a barrel despite the huge EU package.

"Without even getting up to the pre-Greece crisis worry bailout highs and the perhaps renewed confidence in the old reliable greenback, oil may have a hard time regaining those lofty highs," Flynn said.

Adding to market worries was China, the world's second-largest energy consumer after the United States. Official data showed Tuesday that consumer prices rose 2.8 percent in April from a year earlier, putting pressure on Beijing to hike interest rates.

"If the juggernaut that was supposed to carry the world out of recession sputters, the economic 'perfect storm' may be upon us," Mike Fitzpatrick of MF Global warned.

Meanwhile, the OPEC oil producers' cartel on Tuesday held steady its forecast for modest growth in world oil demand this year, noting uncertainty about the global economic outlook.

"Although the economic recovery shows signs of improving momentum, important risks remain that could impact demand growth expectations for this year," the Organization of the Petroleum Exporting Countries (OPEC) said in its May report.

"The world oil demand forecast for 2010 will mostly depend" on the performance of the US economy, the report said.

"Should US oil demand weaken slightly and perform less than expected during the peak summer consumption season, then total world oil demand will be less than the current estimate."

The cartel said it was expecting world oil demand growth to grow by 0.9 million barrels per day (bpd) or 1.1 percent to average 85.4 million bpd for 2010. That was almost unchanged from the previous report.

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