* Canadian dollar at C$1.2345 or 81.00 U.S. cents * Bond prices mixed across the maturity curve TORONTO, June 9 (Reuters) - The Canadian dollar strengthened against its U.S. counterpart on Tuesday, as crude oil prices rose on expectations that the global supply glut would be mitigated by seasonal driving demands and forecasts of falling U.S. shale production. With little on the Canadian domestic calendar, the loonie will likely take its cue from technical and external influences such as crude. * At 8:44 a.m. EDT (1244 GMT), the Canadian dollar was trading at C$1.2345 to the greenback, or 81.00 U.S. cents, stronger than the Bank of Canada's official close of C$1.2398, or 80.66 U.S. cents on Monday. This was its strongest level since May 26. * The currency's strongest level of the session was C$1.2330, while its weakest level was C$1.2442. * U.S. crude prices were up 1.87 percent to $59.23, while Brent crude added 2.06 percent to $63.98. Demand for oil tends to rise over the summer as more drivers take to the roads for holidays in Europe and the United States. There were also some hopes that weak Chinese data will prompt more economic stimulus from the world's second-largest economy. * The Canadian dollar, which was stronger against all of its key currency counterparts, is expected to trade between C$1.2310 and C$1.2380 against the U.S. dollar during Tuesday's North American session, according to RBC Capital Markets. * Canadian government bond prices were mixed across the maturity curve with longer-term bonds falling. The two-year price was down 2 Canadian cents to yield 0.639 percent and the benchmark 10-year fell 30 Canadian cents to yield 1.845 percent. * The Canada-U.S. two-year bond spread was -5.8 basis points, while the 10-year spread was -56.2 basis points. (Reporting by Solarina Ho; Editing by Meredith Mazzilli)