Catalyst for the synthesis of alcohol mixtures containing methanol and higher aliphatic alcohols from CO and H.sub.2, which contains, as an oxide precursor,(a) copper oxide and zinc oxide, which can be transformed into the catalytically active state by reduction with hydrogen;(b) aluminum oxide as a thermostabilizing substance and(c) at least one alkali carbonate or alkali oxide,the oxidic precursor comprising from 20 to 70% of the total volume of pores having a diameter between 14 and 7.5 nm, the alkali content being 13-130.times.10.sup.-6 gram atom alkali metal per gram of the oxidic precursor, and the aluminum oxide component having been obtained from a colloidally dispersed aluminum hydroxide gel or sol.