Medicinal compositions for treating, ameliorating or preventing diseases with sensitivity to 3,6-anhydrogalactopyranose represented by formula (1): ##STR00001## foods, drinks, cosmetics, etc. containing as the active ingredient at least one member selected from the group consisting of the above-mentioned compound, its aldehyde, its hydrate and 2-O-methylated derivatives thereof and soluble sugar compounds containing the above compound. This compound also shows, for example, an apoptosis-inducing activity, a carcinostatic activity and inhibitory activities on the production of active oxygen, lipid peroxide radicals and NO, which makes it useful also as the active ingredient of antioxidants and preservatives.