* Investors position for more ECB stimulus in June
* Lower-rated euro zone debt yields fall to record lows
* Global equity markets decline after record peaks Thursday
* Oil prices ease after gaining on Ukraine tensions
(Adds opening of U.S. markets, byline, dateline; previous LONDON)
NEW YORK, May 9 (Reuters) - The U.S. dollar strengthened against the euro and Japanese yen on Friday after the European Central Bank signaled it could deliver fresh monetary stimulus next month, while global equity markets eased after hitting record peaks this week.
Lower-rated euro zone bonds rallied after ECB President Mario Draghi gave his clearest signal yet that policy-makers might act in June to stem slowing inflation and bolster a fragile economic recovery in the single currency bloc.
Italian and Spanish borrowing costs fell to record lows after the ECB raised the prospect that it could embark on an asset purchase program if inflation remained persistently low.
Spain and Italy, which two years ago were at the forefront of the euro zone debt crisis, badly need the recovery to gain traction to curb high debt levels.
The euro fell 0.53 percent to 1.3767 against the dollar. The dollar basket rose 0.58 percent and the dollar gained 0.11 percent against the yen to 101.76.
John Doyle, currency strategist at Tempus Inc in Washington, said the euro's decline from Thursday has eased a bit and that Draghi in the past has tried to talk down the euro's strength.
"Until the ECB actually acts I don't see a sustained rally in the dollar. The market has been calling Draghi's bluff," Doyle said.
A measure of global equity performance, MSCI's all-country world index, fell 0.48 percent after advancing to its highest level since November 2007 on Thursday.
In Europe, the pan-European FTSEurofirst 300 index slipped 0.4 percent to 1,353.43, after hitting its highest level since May 2008 on Thursday.
On Wall Street, the major stock indices also declined, trading near their level at the beginning of the year. The benchmark S&P 500 is up a bit more than 1 percent for the year, and has traded within a rough 35-point range for two months.
The Dow Jones industrial average fell 34.26 points, or 0.21 percent, to 16,516.71. The S&P 500 lost 7.67 points, or 0.41 percent, to 1,867.96 and the Nasdaq Composite dropped 24.485 points, or 0.6 percent, to 4,027.011.
"We've been trapped in this trading range for several months now," said Bruce Bittles, chief investment strategist at Robert W. Baird & Co in Nashville, Tennessee.
"All the excesses of 2013 are being unwound here in a very, very organized fashion where it's not hurting the popular averages but certainly individual stocks have paid a severe price," Bittles said.
Brent crude gave up initial gains as investors worried that the spreading conflict in Ukraine could disrupt supply from Russia, the world's top oil producer.
Brent crude for June slipped 7 cents to $107.97 a barrel. U.S. oil was up 50 cents at $100.76.
U.S. Treasuries drifted lower as the 30-year long bond again surrendered price gains following an unexpectedly costly $16 billion government auction of new 30-year debt.
Yields on 30-year Treasuries, which have been favored in recent months by pension fund buyers, stood at 3.4413 percent, reflecting a price decline of 6/32.
The benchmark 10-year note fell 4/32 to yield 2.6161 percent.
(Additional reporting by Francesco Canepa in London, reporting by Herbert Lash; editing by Andrew Hay)