The invention relates to a method for preparing polyurethanes containing alkoxysilane groups, said method 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, the at least one compound containing an NCO group and/or the compound containing at least one Zerewitinoff-active H atom containing at least one alkoxysilane group, so as to obtain a polyurethane containing alkoxysilane groups. The invention also relates to a polymer containing alkoxysilane groups, a method for preparing a curable polymer, a curable polymer, a cured polymer, and use thereof. The polyurethanes are prepared with use of a thermally labile tin catalyst.