(Adds BNP FX managers on chances of euro-dollar parity)
* Dollar index hits 11-month high but gains coming harder now
* Euro hits almost 1-year low, political worries keep pressure on
* Aussie, Canadian dollars fall as oil retreats
By Patrick Graham
LONDON, Nov 16 (Reuters) - The dollar inched up to an 11-month high against a basket of currencies on Wednesday and touched its highest in a year against the euro as major banks and investors began to debate the possibility of another move towards dollar parity.
After a week-long rally driven by the post-election surge in U.S. bond yields, some of the major banks were sounding slightly more cautious on the dollar's immediate prospects.
But fuelled by expectations of an inflationary push from the future Trump administration that would spur more rises in Federal Reserve interest rates, it advanced past $1.07 per euro EUR=EBS for the first time since the start of December 2015.
It also rose half a percent against the yen to its highest since June 1, pushing the dollar index .DXY up another 0.2 percent to 100.41. A move above 100.51 would take the index to its highest level since April 2003. It has gained almost 5 percent in just over a week.
Notably, however, St Louis Fed chief James Bullard's comment that it would be a surprise now if the U.S. central bank did not hike rates next month had little impact on the market.
"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 U.S. economic policy under President-elect Trump," said Adam Cole, head of G10 FX strategy with RBC in London.
Trump's victory has raised concern about further, potentially destabilising victories for populists in elections across Europe in the coming year, and a number of banks and traders have predicted the euro will head back towards lows around 1.05 at which the last dollar rally stalled last year.
That also raises the prospect of another attack on parity with the single currency.
"Can the dollar go to parity with the euro? Well we are only 7-8 percent away so probably yes," said Adnan Akant, head of foreign exchange at Fischer Francis Trees and Watts, a New York based institutional currency manager owned by giant French financial group BNP Paribas (PA:BNPP).
"Under Trump, we are looking at fiscal policy divergence (with Europe and Japan) which should be very positive for the dollar. Protectionism is a risk but if that is focused on emerging markets, it may perversely also be a dollar positive."
Against the yen, the dollar gained 0.2 percent to 109.69 yen JPY= , after setting a five-month peak of 109.34 on Tuesday. It gained a third of a percent against sterling GBP= and the Canadian dollar CAD=D4 , and was almost 1 percent higher against the Australian dollar AUD=D4 , weakened by a dip in the price of oil and other major commodities.
"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 Mark Heinrich)