Compounds of the formula I and II ##STR1## where R.sup.1 is hydrogen or an aliphatic, cycloaliphatic, araliphatic, aromatic or heterocyclic radical or an acyl radical, it being possible for these radicals to carry further substituents which do not react with acetylenes or allenes, and the radicals R, independently of one another, are hydrogen or aliphatic, cycloaliphatic, araliphatic, aromatic or heterocyclic radicals which may be linked to one another with formation of a ring and m is 0 or 1, are prepared by an addition reaction of a compound of the formula IIIR.sup.1 OH IIIwith an acetylene or allene of the formula IV or V ##STR2## where R.sup.1 and R have the abovementioned meanings, in the gas phase at elevated temperatures in the presence of a heterogeneous, silicate-containing catalyst, by a process in which the catalyst used contains, as an active component, an X-ray amorphous zinc silicate or cadmium silicate containing from 1 to 40% by weight, calculated as oxide, of zinc or cadmium and is obtainable by applying a zinc salt or cadmium salt of an organic acidic compound which is decomposable at below 400.degree. C., to an amorphous silica and forming the catalyst at from 50 to 500.degree. C., in the presence of a hydroxyl-containing compound selected from the group consisting of water, alkanols with up to 10 carbon atoms, diols and polyols having 2 to 6 carbon atoms and 2 or 3 OH groups and carboxylic acids of 1 to 6 carbon atoms.