The reactions between N-benzyl- and N-methylhydroxylamine and chiral enoate esters, derived from D-glyceraldehyde and (-)-verbenone, respectively, have been investigated. Theoretical calculations show that the most favorable mechanism involves the concerted cycloaddition of the hydroxylamine to the substrate. This result is in good agreement with the stereospecificity observed when the trisubstituted olefins are used. The open-chain adducts have been isolated when the processes are carried out at low temperatures and for short reaction times. These compounds evolve to the corresponding isoxazolidinones on standing at room temperature or under acid catalysis. The high π-facial diastereoselection has been rationalized on the basis of steric effects induced by the dioxolane ring for D-glyceraldehyde derivatives or by the cyclobutane gem-dimethyl substitution for esters prepared from (-)-verbenone. As an application of these reactions, new β-amino acids have been synthesized in a highly efficient and stereocontrolled manner.