Silane-terminated polymers of the formula (I)

Y—[Z—C(═O)—NR3—(CR12)b—SiRa(OR2)3-a]x  (I),

are produced by reacting at least one hydroxy-functional polymer (a), comprising at least one polyether, polyester and/or polyacrylate unit, with at least one compound having at least one isocyanate group, in the presence of at least one bismuth-containing catalyst (K), with the proviso that the reaction mixture comprises 50 to 250 ppm water at the start of the reaction.