The terpenoids 1-3, which posess both intriguing structural features and biological activities (except for 1), contain asymmetric quaternary carbon centers whose efficient and enantio divergent construction is the important issue for the asymmetric total synthesis. We now wish to report the first total synthesis of the marine furanoterpene 1 and the formal total syntheses of (-)-dihydroactinidiolide 2, which exhibits pheromone and phytotoxic activities, and (-)-anastrephin 3, an insect sex attracting pheromone, employing the intramolecular cycloaddition reaction as the key steps. 1. Total Synthesis and Determination of the Absolute Configuration of Furanoterpene 1 The chiral aldehyde 6, which was prepared in an optically active form by using the methodology for assembling the asymmetric quaternary carbon centers developed by Yamamoto, was converted into 1 employing the fused furan construction based on the intramolecular [3+2] cycloaddition of nitrile oxide developed by us. The absolute configuration of the quaternary asymmetric carbon in 1 was determined as S. Alternatively, the intermediate 9 was synthesized more conveniently by using the PLE mediated asymmetric hydrolysis of the functionalyzed prochiral diester 18. 2. Formal Total Syntheses of (-)-Dihydroactinidiolide 2 and (-)-Anastrephin 3 The protected diol 7, an intermediate for the synthesis of 1, was converted into the amide 36a, which was treated with triflic anhydride and collidine to give diastereoselectively (5:1) the bicyclic cyclobutanone 39a via the intramolecular [2+2] cycloaddition of the in situ generated keteniminium salt 37a in 68% yield. The major diastereomer was converted into the lactone 41, an easily convertible immediate precursor to 2. For the synthesis of anastrephin 3, the olefinic lactone 48, a key intermediate for the total synthesis of Tadano, was synthesized similarly via the [2+2] cycloaddition of the nor-keteniminium salt generated from 45. However, the efficiency of 1,2-asymmetric induction during the cycloaddition is disappointingly low (2:1).