* CAD rallies vs Aussie, GBP, supported vs USD
* Conservatives' vote win quells political uncertainty
* Analysts expect CAD to extend broad gains
LONDON, May 3 (Reuters) - The Canadian dollar rallied on Tuesday after Canada's Conservative party clinched an outright election victory, and the currency was poised for more gains as the majority win erased fears of political instability.
The Canadian currency hovered near a 3 1/2-year high against the U.S. dollar. It also rallied against the Australian dollar, which relinquished gains made during the election campaign as the pro-worker New Democratic Party soared in popularity.
The ruling Conservatives secured 54 percent of seats in the G7 country's parliament on Monday, resulting in a majority government which offers Prime Minister Stephen Harper free reign to keep corporate taxes low and a tight grip on public spending. [ID:nN03272319]
"It's positive that Canada now has an outright majority government," said Adam Cole, global head of FX strategy at RBC.
"The general trend during the campaign was of CAD underperformance ... which was driven by the uncertainty surrounding the surging support for the New Democrat Party. What we should see now is that trade unwinding."
Investors had dumped the Canadian dollar versus its Australian counterpart in the past month after swelling support for the NDP raised the nightmare scenario for markets of an unstable minority government headed by the left-leaning party.
The Canadian dollar was broadly supported in European trade, with the U.S. dollar CAD=D4 hovering around $0.9500, not far from the day's low of $0.9460.
Broad weakness in the U.S. currency has offered a boost to the Canadian dollar, which climbed as high as C$0.9440, its strongest since late 2007.
"CAD can now play catch-up both against the USD and indeed against its commodity cousins," BNP Paribas analysts said in a note. "A break of support at C$0.9450 opens the way towards the November 2007 low at C$0.9071.
The Australian dollar AUDCAD=R fell around half a percent on the day to A$1.0338, retreating from $1.0443 hit late last week, its strongest since early 2004.
Cole at RBC said he expected the Aussie's near term retreat to extend to around A$1.02, a key pivot level which acted as resistance to the Aussie's uptrend on two occasions in late 2010.