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How long can Treasury yields stay this low?

The sharp fall in U.S. Treasury yields this year has taken many by surprise, and some traders are now looking for the exits amid concern that a correction is looming.

"The kitchen is about to heat up and we want out now," Morgan Stanley said in a note Friday.

It believes expectations the European Central Bank (ECB) will take fresh easing measures are behind the decline in Treasury yields over April and May and that the central bank's policy decision on Thursday will mark the low for yields.

Read More 'Mysterious' bond market move could continue

"Investors have been lured into Treasurys by ECB President Draghi's honey-sweet siren song. Strap yourself to the mast and increase duration underweights ahead of the ECB," it said.

In addition to the ECB, traders have pointed to a variety of factors including short-covering spurred by a "bear squeeze" and a flight to safety amid global economic jitters for the rally in U.S. Treasury prices, which move inversely to yields.

After touching 11-month lows of 2.44 percent last week, U.S. 10-year Treasury yields had edged up to 2.49 percent by early Monday, well off the highs of around 3.0 percent touched in early January.

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While many analysts expect the run-up in Treasury prices could continue, others are skeptical.

"Everyone now seems to be more bullish on the bond market," Don Smith, a strategist at ICAP, told CNBC last week. "It makes me worry that at some point there will be quite a sharp correction," he said, citing the continuing recovery in the U.S. economy.

"At some point, there has to be a response in the inflation environment," which would mean the U.S. Federal Reserve would need to move to a more normal interest rate policy, he said.

Smith isn't alone in believing the U.S. economic environment isn't conducive to keeping Treasury yields under the cosh.

Read More This is what is keeping bond yields low

"A 30-year bond close to 3 percent and a 10 year at 2.4 percent are just too rich for our taste," Patrick Perret-Green, a senior strategist at ANZ, said in a note Thursday. "More than a few measures suggest that the risks of upside surprises are increasing," he said, citing positive U.S. economic data released over the past week, including new home sales, durable goods orders and commercial lending.

"Now is the time to be reducing duration and that returns in the long end over the remainder of the year are likely to be negative," he said, noting ANZ has closed out several positions.

Some even believe both long and short positions on the Treasury market are problematic.

Read More Bond market in lull, but are yields bottoming?

"U.S. Treasurys probably are at the insider profit-taking stage for those who are long, while they have recently entered the 'panic' stage for those who are short," Deutsche Bank said in a note last week analyzing where various assets fall in the Minsky cycle.

The cycle tracks assets through the stages of undervaluation due to macro shock displacement, followed by a healthy expansion, leverage-driven gains, euphoria, insider profit-taking, liquidation and panic, and finally revulsion.

—By CNBC.Com's Leslie Shaffer; Follow her on Twitter @LeslieShaffer1

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