Process for producing alkoxysilane-containing polyurethanes comprising the step of reacting a compound containing at least one NCO group with a compound containing at least one Zerewitinoff-active H atom in the presence of a catalyst component, wherein the compound containing at least one NCO group and/or the compound containing at least one Zerewitinoff-active H atom contain at least one alkoxysilane group, to afford an alkoxysilane-containing polyurethane, characterized in that the catalyst component contains a complex of ytterbium with at least one beta-diketonate ligand, wherein the latter is obtainable by deprotonation of hacac (acetylacetone), hacac-F 7 (perfluoroacetylacetone), hbfa (benzoyl-2-furanoylmethane), hbpp (l,3-bis(3-pyridyl)-1,3-propanedione), Hbtfac (benzoyltrifluoroacetone), hbzac (benzoylacetone), hdbbm (di(4-bromo)benzoylmethane), hdcm (d,d-dicampholylmethane), hdmbm (4,4'-dimethoxydibenzoylmethane), hdmh (2,6-dimethyl-3,5-heptanedione), hdnm (dinaphthoylmethane), hdpm (dipivaloylmethane), hdppm (di(perfluoro-2-propoxypropionyl)methane), hdtp (1,3-di(2-thienyl)-1,3-propanedione), hfacam (3-(trifluoroacetyl)-d-camphor), hfdh (6,6,6-trifluoro-2,2-dimethyl-3,5-hexanedione), hfhd (1,1,1,2,2,6,6,7,7,7-decafluoro-3,5-heptanedione), hfod (6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedione), hftac (2-furyltrifluoroacetone), hhfac (hexafluoroacetylacetone), hhfbc (3-(heptafluorobutyryl)-d-camphor), hhfth (4,4,5,5,6,6,6-heptafluoro-1-(2-thienyl)-1,3-hexanedione), hmfa (4-methylbenzoyl-2-furanoylmethane), hmhd (6-methyl-2,4-heptanedione), hntac (2-naphthoyltrifluoroacetone), hpop (3-(5-phenyl-1,3,4-oxadiazol-2-yl)-2,4-pentanedione), hppa (3-phenyl-2,4-pentanedione), hpta (=htpm) (pivaloyltrifluoroacetone), hptp (1-phenyl-3-(2-thienyl)-1,3-propanedione), H(t-cam) (3-(tert-butylhydroxymethylene)-d-camphor), htfac (trifluoroacetylacetone), htfn (l, l, l, 2, 2, 3, 3, 7, 7, 8, 8, 9, 9, 9-tetradecafluoro-4, 6-nonanedione), hthd (=hdpm, htmhd) (2,2,6,6-tetramethyl-3,5-heptanedione), htnb (4,4,4-trifluoro-1-(2-naphtyl)-1,3-butanedione), htmod (2,2,6,6-tetramethyl-3,5-octanedione), htrimh (2,2,6-trimethyl-3,5-heptanedione), htod (2,2,7-trimethyl-3,5-octanedione), htta (2-thenoyltrifluoroacetone) or any desired mixture thereof and in that the catalyst component is free from organic tin compounds, wherein the content of the ytterbium beta-diketonate complex based on the total weight of the components employed in the reaction is ≥ 0.0001% by weight to ≤ 1% by weight. a compound containing at least one NCO group with a compound containing at least one Zerewitinoff-active H atom in the presence of a catalyst component, wherein the compound containing at least one NCO group and/or the compound containing at least one Zerewitinoff-active H atom contain at least one alkoxysilane group, to afford an alkoxysilane-containing polyurethane, characterized in that the catalyst component contains a complex of ytterbium with at least one beta-diketonate ligand, wherein the latter is obtainable by deprotonation of hacac (acetylacetone), hacac-F 7 (perfluoroacetylacetone), hbfa (benzoyl-2-furanoylmethane), hbpp (l,3-bis(3-pyridyl)-1,3-propanedione), Hbtfac (benzoyltrifluoroacetone), hbzac (benzoylacetone), hdbbm (di(4-bromo)benzoylmethane), hdcm (d,d-dicampholylmethane), hdmbm (4,4'-dimethoxydibenzoylmethane), hdmh (2,6-dimethyl-3,5-heptanedione), hdnm (dinaphthoylmethane), hdpm (dipivaloylmethane), hdppm (di(perfluoro-2-propoxypropionyl)methane), hdtp (1,3-di(2-thienyl)-1,3-propanedione), hfacam (3-(trifluoroacetyl)-d-camphor), hfdh (6,6,6-trifluoro-2,2-dimethyl-3,5-hexanedione), hfhd (1,1,1,2,2,6,6,7,7,7-decafluoro-3,5-heptanedione), hfod (6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedione), hftac (2-furyltrifluoroacetone), hhfac (hexafluoroacetylacetone), hhfbc (3-(heptafluorobutyryl)-d-camphor), hhfth (4,4,5,5,6,6,6-heptafluoro-1-(2-thienyl)-1,3-hexanedione), hmfa (4-methylbenzoyl-2-furanoylmethane), hmhd (6-methyl-2,4-heptanedione), hntac (2-naphthoyltrifluoroacetone), hpop (3-(5-phenyl-1,3,4-oxadiazol-2-yl)-2,4-pentanedione), hppa (3-phenyl-2,4-pentanedione), hpta (=htpm) (pivaloyltrifluoroacetone), hptp (1-phenyl-3-(2-thienyl)-1,3-propanedione), H(t-cam) (3-(tert-butylhydroxymethylene)-d-camphor), htfac (trifluoroacetylacetone), htfn (l, l, l, 2, 2, 3, 3, 7, 7, 8, 8, 9, 9, 9-tetradecafluoro-4, 6-nonanedione), hthd (=hdpm, htmhd) (2,2,6,6-tetramethyl-3,5-heptanedione), htnb (4,4,4-trifluoro-1-(2-naphtyl)-1,3-butanedione), htmod (2,2,6,6-tetramethyl-3,5-octanedione), htrimh (2,2,6-trimethyl-3,5-heptanedione), htod (2,2,7-trimethyl-3,5-octanedione), htta (2-thenoyltrifluoroacetone) or any desired mixture thereof and in that the catalyst component is free from organic tin compounds, wherein the content of the ytterbium beta-diketonate complex based on the total weight of the components employed in the reaction is ≥ 0.0001% by weight to ≤ 1% by weight.