Titanium silicate molecular sieve, TS-1, has been found to be a highly efficient and selective catalyst in dihydroxylation of olefins under triphase reaction conditions in the presence of dilute hydrogen peroxide. Among the substrates unsaturated alcohols (greater than or equal to C-4) give selectively corresponding triol in a very high yield with very high H2O2 efficiency. Unsaturated halides give the corresponding diols even at a faster reaction rate. Whereas under the conventional biphase system (in the presence of a cosolvent to homogenize the liquid layers) epoxide is obtained as the major final product in high yield. The substrate nature, i.e., steric hindrance at the active site and hydrophobicity/hydrophilicity of both substrate and epoxide intermediate, is considered to account for the product distribution. Acidity generated in situ over TS-1 in the presence of water (used as the dispersion medium) is responsible for the bifunctional (oxidation and acidic) behavior of the titanium silicate.