* C$ at C$1.0071 to the US$, or 99.30 U.S. cents
* Domestic trade surplus offset by U.S. jobless claims
* ECB rate cut boosts both North American currencies
TORONTO, May 2 (Reuters) - The Canadian dollar strengthened against its U.S. counterpart on Thursday after the domestic economy posted a surprise trade surplus, though the gain was trimmed by greenback appreciation after a sharp fall in jobless claims.
"The problem for the Canadian (dollar) ... has been the fact that at the same time, we saw a much better than expected jobless claims number out of the U.S," said Jeremy Stretch, head of foreign exchange strategy at CIBC World Markets.
The currency firmed to C$1.0060 to the greenback, or 99.40 U.S. cents, after Statistics Canada said growing exports led to a C$24 billion surplus in March.
It closed at C$1.0081, or 99.20 U.S. cents on Wednesday.
But the greenback also gained, pushing the loonie back to around C$1.0071, or 99.30 U.S cents, as fewer Americans filed new claims for unemployment benefits than at any time in the last five years.
The North American currencies both gained versus the euro after the European Central Bank cut interest rates for the first time in 10 months, driven to act by an economy wallowing in recession and freed to do so by sharply falling inflation.
Stretch said that if U.S. non-farm payrolls data due out on Friday followed the jobless claims data with a positive surprise, the loonie could bounce as much as a cent higher, but would struggle to weaken much beyond C$1.02 this week.
Prices for Canadian government debt were mixed, with the two-year bond off half a Canadian cent to yield 0.918 percent and the benchmark 10-year bond rising 5 Canadian cents to yield 1.679 percent.