* U.S. yields, dollar fall after bill collapses

* Investors temper expectations for Trump's spending plans

* Euro zone yields track move but supply weighs

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr

By John Geddie

LONDON, July 18 (Reuters) - Europe's benchmark bond yields edged down on Tuesday, tracking U.S. equivalents after the collapse of a second healthcare bill in the U.S. Senate showed the difficulties President Donald Trump faces passing his ambitious spending plans.

Yields across the globe rose sharply after Trump won the U.S. election in November on promises for tax reforms and infrastructure investment that were expected to boost growth and inflation in the world's largest economy.

However, for most of this year, yields have been grinding lower as investors tempered expectations both for the speed at which Trump's plans can be implemented and the pace of monetary tightening by the U.S. central bank.

"It is further evidence that not much will come from (Trump's) pro-growth policy that he pledged when he came to power. The market reaction is consistent but it is fairly small suggesting a lot of this had already been priced in," KBC strategist Piet Lammens said.

The announcement on Monday that two Republican Senators would not support the latest version of the healthcare bill -- meaning it does not have enough votes to pass -- was yet another blow for Trump.

U.S. 10-year bond yields and the dollar immediately fell after the news, while German 10-year yields dipped 2 basis points to 0.57 percent when European trading started on Tuesday.

Most other euro zone yields were flat or 1-2 bps lower.

Analysts said further falls would be kept in check by upcoming supply which tends to put upward pressure on yields as investors sell outstanding bonds to make room in their portfolios for new debt.

Europe's bailout fund - the European Financial Stability Facility - mandated a group of banks on Monday for a dual-tranche bond sale, a deal expected to come to market on Tuesday.

There is also widespread speculation that Greece will end a three-year exile from markets this week and sell new debt. Greece is said to be looking at selling 2-4 billion euros of five-year bonds, Thomson Reuters' IFR reported.

For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets ($1 = 0.8679 euros)

(editing by John Stonestreet)