Composition comprising olefinically functionalized siloxane oligomers having not more than one olefinic radical on the silicon atom, characterized in that - the olefinically functionalized siloxane oligomers have Si-O-crosslinked structural elements which form catenary, cyclic, crosslinked or optionally three-dimensionally crosslinked structures, with at least one structure corresponding to the general formula I, (R 1 O) [(R 1 O) 1-x (R 2) x Si O] a [Si 2 O] c [Si (R 4) y (OR 3) 1-y O] b R 3, - wherein the structural elements are derived from alkoxysilanes and - A in the structural element corresponds to an olefinic radical and is selected from a linear, branched or cyclic alkenyl- or cycloalkenyl-alkylene-functional group having in each case 2 to 16 C atoms and - B in the structural element corresponds to a saturated hydrocarbon radical and is selected from a linear, branched or cyclic alkyl radical having 1 to 16 C atoms, - Y corresponds to OR 3 or, in crosslinked and optionally three-dimensionally crosslinked structures, independently of one another, to OR 3 or O 1/2, - where R 1 independently at each occurrence corresponds to a linear, branched or cyclic alkyl radical having 1 to 4 C atoms or H, - R 3 independently at each occurrence corresponds to a linear, branched or cyclic alkyl radical having 1 to 4 C atoms or to H, and R 2 corresponds independently at each occurrence to a linear, branched or cyclic alkyl radical having 1 to 15 C atoms, R 4 corresponds independently at each occurrence to a linear, branched or cyclic alkyl radical having 1 to 15 C atoms, - a, b, c, x and y independently correspond to integers with 1 ≤ a, 0 ≤ b, 0 ≤ c, x independently at each occurrence is 0 or 1, y independently at each occurrence is 0 or 1, and (a+b+c) ≥ 2, - the total chloride content being less than or equal to 250 mg/kg and - the structural elements [(R 1 O) 1-x (R 2) x Si O] a, [Si (R 4) y (OR 3) 1-y O] b and [Si 2 O] c in the general formula I being present together, in relation to all silicon atoms of the general formula I, at greater than or equal to 10% as T structure. - the olefinically functionalized siloxane oligomers have Si-O-crosslinked structural elements which form catenary, cyclic, crosslinked or optionally three-dimensionally crosslinked structures, with at least one structure corresponding to the general formula I, (R 1 O) [(R 1 O) 1-x (R 2) x Si O] a [Si 2 O] c [Si (R 4) y (OR 3) 1-y O] b R 3, - wherein the structural elements are derived from alkoxysilanes and - A in the structural element corresponds to an olefinic radical and is selected from a linear, branched or cyclic alkenyl- or cycloalkenyl-alkylene-functional group having in each case 2 to 16 C atoms and - B in the structural element corresponds to a saturated hydrocarbon radical and is selected from a linear, branched or cyclic alkyl radical having 1 to 16 C atoms, - Y corresponds to OR 3 or, in crosslinked and optionally three-dimensionally crosslinked structures, independently of one another, to OR 3 or O 1/2, - where R 1 independently at each occurrence corresponds to a linear, branched or cyclic alkyl radical having 1 to 4 C atoms or H, - R 3 independently at each occurrence corresponds to a linear, branched or cyclic alkyl radical having 1 to 4 C atoms or to H, and R 2 corresponds independently at each occurrence to a linear, branched or cyclic alkyl radical having 1 to 15 C atoms, R 4 corresponds independently at each occurrence to a linear, branched or cyclic alkyl radical having 1 to 15 C atoms, - a, b, c, x and y independently correspond to integers with 1 ≤ a, 0 ≤ b, 0 ≤ c, x independently at each occurrence is 0 or 1, y independently at each occurrence is 0 or 1, and (a+b+c) ≥ 2, - the total chloride content being less than or equal to 250 mg/kg and - the structural elements [(R 1 O) 1-x (R 2) x Si O] a, [Si (R 4) y (OR 3) 1-y O] b and [Si 2 O] c in the general formula I being present together, in relation to all silicon atoms of the general formula I, at greater than or equal to 10% as T structure.