GRAPHIC-Trump, Draghi, Fed doubts: is the dollar rally done?

* Dollar rallies since Bretton-Woods: http://tmsnrt.rs/2g7ph8E

* Last five years of USD strength: http://reut.rs/2sQLLmZ

By Patrick Graham and Ritvik Carvalho

LONDON, June 28 (Reuters) - If shifts in major banks' currency views are anything to go by, Tuesday's speech by European Central Bank Governor Mario Draghi may mark an early end to the dollar's third big rally since the late 1970s.

Barclays (LSE: BARC.L - news) and Deutsche Bank (IOB: 0H7D.IL - news) , along with Goldman Sachs (NYSE: GS-PB - news) , led the charge in 2014 in predicting rises in U.S. interest rates and the weakness of Europe would see the greenback reach parity with the euro for the first time in more than a decade.

Yet instead, Draghi's cementing of expectations for a gradual tightening of euro zone monetary policy - and the lack of faith in the Fed's promises on rate rises - spurred a 2 percent jump in the euro this week that to some felt final.

Both Barclays and Deutsche - respectively the fifth and seventh biggest players in the $5 trillion a day global currencies trade - have now backed off long-held support for the greenback in the space of a few days.

"The prospective economic and monetary divergence that has driven the dollar updraft has peaked," Barclays' macro research team said in a note last Thursday.

"It seems premature ... to call for a dollar downdraft. But with the USD already significantly overvalued on most of our metrics (by about 15 percent), medium-term risks are mainly to the downside," they added.

Many economists already believed the greenback was nearing the end of the road last year when excitement over the boost to spending and growth promised by President Donald Trump funded one last hurrah.

The evaporation of faith in that idea along with Trump's troubles in Congress over healthcare have pulled the greenback 10 cents back from the long-term highs of $1.03 per euro hit in January.

Strength against a batch of other emerging currencies has kept the index used to measure its broader strength rising.

But if this week's moves mark the end of the line, the 24 percent gain this time will have fallen well short of previous rallies between 1995 and 2002 and 1978 and 1985, when the dollar gained respectively 53 and 34 percent.

(Graphics by Ritvik Carvalho and Vincent Flasseur Editing by Jeremy Gaunt.)