Asymmetric homo-cyclodimerization of oxabicyclic alkenes proceeded with high efficiency in the presence of a cationic rhodium/(R)-binap catalyst to give high yields of chiral tetrahydrofurans of up to 99% ee. The cationic rhodium complex also catalyzed the asymmetric cross-cyclodimerization between oxabicyclic alkenes and dimethyl 2-butynedioate, which gave dihydrofurans as [3 + 2] cycloadducts with high enantioselectivity (99% ee).