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FOREX-Euro eases below $1.36, dollar rises as sterling stumbles

* Euro weakens again as traders eye policy shifts

* Sterling and euro dip below closely watched levels

* Dollar upswing may continue, says analyst (Adds late price details, comments)

By Michael Connor

NEW YORK, May 28 (Reuters) - The dollar climbed on Wednesday, extending a rally that began last week as the euro and sterling slipped beneath recent lows that may signal more gains for the greenback.

Getting a lift from positive housing data published on Tuesday, the U.S. dollar index hit a new eight-week peak of 80.581. The measure of a basket of currencies was last at 80.566 in late New York trade, up 0.27 percent.

After knocking on $1.40 in recent weeks, the euro was off 0.3 percent to $1.3593, beneath the psychologically significant $1.36 level. It was also down against the yen.

The pound, too, declined and traded as low as $1.6699 , a hair beneath $1.67 and a level under a recent bottom that some analysts said may foretell further declines in sterling. It was last at $1.6708, off 0.6 percent for the trading day.

Sterling has been hit in recent days by a combination of slightly weaker economic data and hints of growing political threats to Britain's long-term status quo. It had risen 2.12 percent against the dollar in the last six months.

"Most of today's trading was within small increments but the moves in the euro and pound are significant," said Camilla Sutton, currency strategist at Scotia Capital in Toronto. "We may now see the rally in the dollar everyone expected at the start of the year."

The yen was down 0.15 percent against the dollar.

Sutton said global investors on Wednesday were focused on bond markets, where the yield on the benchmark U.S. 10-year Treasury note fell to an 11-month low at 2.434 percent. The yield on the 30-year bond hit a low not seen in nearly a year.

Investors have been buying long-dated debt in tandem with declines in European yields and as reduced Federal Reserve purchases of bonds are expected to increase the duration in indexes many bond fund managers track.

"The market likes the dollar at the moment even though Treasury yields are lower. If they start to rally, as I think they will, then the dollar may take off," said Graham Davidson, a currency dealer with NAB in London.

Sterling early on Wednesday had sunk below a key technical support and was vulnerable to further declines, according to FXDD currency analyst Greg Michalowski.

"It broke through the 1.6770 level on the daily chart, and I pay attention to that," Michalowski said.

(Reporting by Michael Connor; Editing by Chizu Nomiyama and James Dalgleish)