Herein are disclosed a process for increasing in purity, or purifying, an N-protected-.beta.-aminoalcohol which process comprises (i) adding water to a polar organic solvent in which an N-protected-.beta.-aminoalcohol such as a (2R,3S)- or (2S,3R)-3-tert-butoxycarbonylamino-1-halo-2-hydroxy-4-phenylbutane or the like, or (ii) crystallizing such an N-protected-.beta.-aminoalcohol from a diol or a diol-based mixed solvent, and a process for producing the corresponding N-protected-.beta.-aminoepoxide which process comprises treating, with a base, the thus purity-enhanced N-protected-.beta.-aminoalcohol. Such N-protected-.beta.-aminoalcohols and N-protected-.beta.-aminoepoxides are both useful as synthetic intermediates for medicine compounds, such as, e.g., HIV protease inhibitor and the like.