The dollar is being supported by improving U.S. economic data, which reduces the likelihood of further stimulus from the Federal Reserve. Oil prices, seen as the big risk to the global economic outlook, dipped to just below $125 a barrel after gaining $3 on Friday but no new catalysts emerged to further boost risk appetite and push stocks higher.

U.S. stocks had their best week in three months last week and European shares climbed to peaks not seen since last July after waves of central bank liquidity eased concerns about the economic outlook and risks from the euro zone debt crisis eased.

German Bunds suffered a sell-off last week on rising optimism about the global outlook and easing concerns about the euro zone debt crisis, but they rebounded on Monday with analysts saying more good news on the global economy would be needed to push them below this year's lows.

The political environment in Europe leading up to forthcoming French and Greek elections, as well as high oil prices and concerns about the strength of growth in Asia are all lingering uncertainties weighing on sentiment in global markets.

"We think the (equity) rally has a bit more legs yet but there's no doubt that it is not going to get there in a straight line," Barclays Wealth Equity Strategist William Hobbs said.

Hobbs singled out the healthy state of many corporate balance sheets as a key factor supporting riskier assets.

"We still think the prospects for earnings growth are reasonable. Alongside this, stock markets are very inexpensive still ... and also central banks are likely to remain helpful for a while yet."

U.S. computer giant Apple (AAPL.O), the world's most valuable company, is sitting on $98 billion of cash thanks to strong sales of its iconic consumer products, and plans to reveal how it will spend the cash later today.

The FTSE Eurofirst .FTEU3 index of top European shares opened down 0.4 percent at 1,104.04 points after climbing for the fourth straight day on Friday and hitting its highest level since before the market's slump in late July.

European bank shares were coming under pressure as the process to settle outstanding Greek credit default insurance was being held, expected to pay out $2.5 billion to holders of the protection.

The MSCI world equity index .MIWD00000PUS, helped by good gains in Asian markets on Monday, was off about 0.1 percent 335.61, marking a rise of over 12 percent for the year so far.

Currency markets were held in check by a generally firm dollar which has been underpinned by the Federal Reserve's positive outlook for the U.S. recovery and signs its is holding off from further monetary policy easing for now.

The euro was down 0.2 percent at around $1.3150, while the dollar measured against a basket of major currencies .DXY was 0.1 percent higher at 79.84.

With Greek-related risks in the euro zone taking a breather for now, the euro was supported against the yen, while the Federal Reserve's not-so-dovish outlook was giving U.S. dollar bulls a boost, said Jeremy Stretch, head of currency strategy at CIBC World Markets.

Japanese markets will be shut for a holiday on Tuesday.

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Apple cash mountain: link.reuters.com/veq27s

Global real bond yields: link.reuters.com/byn65s

Equities correlation to dlr: link.reuters.com/dek27s

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OIL PRICE WORRY

The price of oil remains the big risk factor to the brighter global economic outlook with tougher Western sanctions against Iran for its nuclear programme due to come into effect on July 1, potentially disrupting middle East supplies.

While Brent crude dropped below $125 a barrel on Monday it remains high due to the Iran concerns with analysts saying the market is still factoring in the full risk of a major supply squeeze.

Higher output from top exporter Saudi Arabia and plans by Iraq to expand its export routes have tempered some of the fears.

"It's a question of whether other producers can handle a significant supply disruption," said Ric Spooner, chief market analyst at CMC Markets in Sydney.

The improved economic outlook saw U.S. Treasury and German Bund prices fall sharply last week with yields expected to keep moving higher as more evidence of recovery emerges, encouraging more investors to move into higher yielding debt.

But on Monday the recent sell-off was encouraging some investors who fear the euro zone debt crisis is far from over.

German 10-year yields were last 3.8 basis points lower on the day at 2.02 percent while 10-year U.S. Treasury note yields fell 2.9 basis points to 2.27 percent.

Selling pressure on German Bunds, which increases their yield, could resume if flash euro zone manufacturing and service surveys due on Thursday show signs that the bloc's economy was keeping pace with the United States.

(Editing by John Stonestreet and Susan Fenton)

• A Permanent Economic Emergency