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 effects, were synthesized stereoselectively starting from (S)-pyroglutamic acid derivatives. alpha,beta-Unsaturated lactams ((S)-5-hydroxymethyl-2-oxo-3-pyrroline derivatives), alpha,beta-unsaturated delta-lactone ((S)-4-amino-2-penten-5-olide derivative), and E-olefin ((S,E)-methyl-4-amino-5-hydroxypent-2-enoate derivative) from (5) -pyroglutamic acid derivatives were dihydroxylated using OsO4 in the presence of N-methyl morpholine N-oxide (NMO) to afford various chiral building blocks with different configurations. The stereoselectivity of cis-dihydroxylation for alpha,beta-unsaturated lactams and alpha,beta-unsaturated delta-lactone was very high, while the stereoselectivity was low for E-olefin. Therefore, the double asymmetric induction of E-olefin using K-2 OsO4 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 alpha,beta-unsatulated lactam. (+)-1-Deoxynojirimycin was synthesized from a (28,3R,4R)-methyl 4-amino-2,3,5-trihydroxypentanoate derivative of E-olefin. (-)-Swainsonine and its stereoisomers were synthesized from (2R,35,4R) - or (2R,3R,4R)-2-hydroxymethyl-3,4-dihydroxypyrrolidine derivatives of alpha,beta-unsaturated delta-lactone or alpha,beta-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 alpha-aminocarbonyl group or beta-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,55)-2,3-dihydroxymethyl-3,4-dihydroxyl pyrrolidine derivatives of alpha,beta-unsaturated lactam.