A cationic rhodium(I)-BINAP complex catalyzed enantioselective [2+2+2] cycloaddn. of a tosylamide-linked 5-allenal H2C:C:CHCH2N(X)CH2CHO (X = Ts) and 5-allenone H2C:C:CHCH2N(X)CH2C(O)CH3 with internal alkynes leading to the formation of bicyclic oxygen heterocycles I (R1 = H, CH3; R2 = C(O)CH3, Si(CH3)3, CH2CH3, etc.; R3 = Me, Et, i-Pr, etc.). [on SciFinder(R)]