The catalyst can be prepared by reduction of a precursor of a hydrogenation-active metal, which may be present on an oxidic support, by reaction with at least one compound of the formula (I)

H_nM(OR)_3-n  (I)

where

M is Ga or Al,

R is CR₃ or SiR₃ where R is C_1-20-alkyl, and

n is 1 or 2,

or dimers or oligomers thereof, wherein the crystallite size of the hydrogenation-active metal in the finished catalyst is from 5 to 30, preferably 5 to 15 nm.