Naturally occurring polyhydroxylated amines such as (+)-1-deoxynojirimycin, polyoxamic acid, anisomycin, (-)-swainsonine, and alexine stereoisomers, which have interesting biological activities including glucosidase-and mannosidase-inhibitory activity, immunoregulatory activity, and antibacterial eŠects, were synthesized stereoselectively starting from (S )-pyroglutamic acid derivatives. a,b-Unsaturated lactams ((S )-5-hydroxymethyl-2-oxo-3-pyrroline derivatives), a,b-unsaturated d-lactone ((S )-4-amino-2-penten-5-olide derivative), and E-oleˆn ((S,E )-methyl-4-amino-5-hydroxypent-2-enoate derivative) from (S )-pyroglutamic acid derivatives were dihydroxylated using OsO 4 in the presence of N-methyl morpholine N-oxide (NMO) to aŠord various chiral building blocks with diŠerent conˆgura-tions. The stereoselectivity of cis-dihydroxylation for a,b-unsaturated lactams and a,b-unsaturated d-lactone was very high, while the stereoselectivity was low for E-oleˆn. Therefore, the double asymmetric induction of E-oleˆn using K 2 OsO 4 with chiral ligands was successively applied to yield high stereoselectivity. (2R,3S )-2-Hydroxymethyl-3-hydroxypyrrolidine and Gaissman-Weiss lactone, important intermediates for the preparation of pyrrolizidine alkaloids, were synthesized from a (3R,4R,5R )-3,4-dihydroxy-5-hydroxymethyl-2-pyrrolidinone derivative derived from a,b-unsatulated lactam. (+)-1-Deoxynojirimycin was synthesized from a (2S,3R,4R )-methyl 4-amino-2,3,5-trihydroxypentanoate derivative of E-oleˆn. (-)-Swainsonine and its stereoisomers were synthesized from (2R,3S,4R)-or (2R,3R,4R )-2-hydroxymethyl-3,4-dihydroxypyrrolidine derivatives of a,b-unsaturated d-lactone or a,b-unsaturated lactam. The key reaction was diastereoselective allylation of the aldehyde derived from the corresponding 2-hydroxymethylpyrrolidine derivatives with various allylation reagents. The high diastereoselectivity could be explained by cyclic chelate formation between metals and the a-aminocarbonyl group or b-alkoxycarbonyl group, in which the nucleophile approaches from the less hindered face. Four alexine stereoisomers were synthesized from (2R,3R,4S,5R )-and (2R,3R,4S,5S )-2,3-dihydroxymethyl-3,4-dihydroxyl pyrrolidine derivatives of a,b-unsaturated lactam.