(New throughout after start of European trade)
* Dollar index flattens out just below Tuesday's 11-month high
* Euro hits almost 1-year low, political worries keep pressure on
* Banks more cautious on broad dollar gains
By Patrick Graham
LONDON, Nov 16 (Reuters) - The dollar steadied just off an 11-month high against a basket of currencies on Wednesday, with major banks sounding slightly more divided on its immediate prospects after a week-long rally driven by the post-election surge in U.S. bond yields.
The dollar index .DXY slipped just 0.1 percent to 99.989, easing from Tuesday's high of 100.26 but still almost 5 percent higher than a trough hit before Donald Trump won the race for the White House a week ago.
Fuelled by expectations of an inflationary push from the new administration that would prompt more rises in Federal Reserve interest rates it was back on the rise against the euro in early trade in London. A move above 100.51 would take the index to its highest since April 2003.
"Broad gains are clearly meeting more resistance, as a December Fed hike is now 95 percent discounted and much uncertainty still surrounds the broader direction of US economic policy under President-elect Trump," said Adam Cole, head of G10 FX strategy with RBC in London.
"Widespread reports that infighting among the transition team is hampering the formation of the government are probably not helping."
The U.S. result has raised worries of another round of potentially destabilising victories for populists in elections across Europe in the coming year, and some banks and traders believe the euro will head back towards lows around 1.05 at which the last dollar rally stalled last year.
The single currency hit $1.0700, its lowest since the start of December last year, as trade got going in London.
"A bit of a euro short-covering rally overnight changes nothing," said Societe Generale (PA:SOGN) strategist Kit Juckes.
"The $1.0580 area where the last two euro falls have found resistance is the next key support. There's a huge dose of political concern to keep the pressure on the euro ahead of the Italian referendum on 4 Dec, and perhaps ahead of French elections next year too."
Against the yen, the dollar gained 0.2 percent to 109.46 yen JPY= , after setting a five-month peak of 109.34 on Tuesday. It was marginally weaker against sterling and the Canadian dollar.
"Buy dollars is still probably the main trade," said a senior trader with another international bank in London.
"The initial knee-jerk trade has run its course now. We might see some to-and-froing, but in general the dollar should stay strong. I don't know about parity with the euro but we may definitely take another crack at $1.05." (Editing by Hugh Lawson)