Silicone composition A comprising a silicone base B capable of crosslinking or curing by polyaddition and characterized in that it comprises an adhesion promoter system D comprising at least one organic titanium compound M and at least one additive X which is a linear organopolysiloxane comprising siloxyl units (I.1) to ( I.3) having the formulae below: - Y a Z b 1 SiO 4 − a + b 2 - Z 3 2 SiO 1 2 - H d Z e 3 SiO 4 − d + e 2 and not comprising units of formula (1.4): - Z 2 2 SiO 2 2 in which - a=1 and b=1 or 2 - d=1 and e=1 or 2 - the symbol Y represents a radical comprising a hydrocarbon-based group having from 2 to 20 carbon atoms and an epoxy function, with optionally one or more heteroatoms such as an oxygen atom, preferably the symbol Y is chosen from the radicals consisting of the group: alkyl glycidyl ether, linear, branched or cyclic epoxyalkyl, linear, branched or cyclic epoxyalkenyl and carboxylic acid glycidyl ester, - the symbols Z 1, Z 2 and Z 3, which may be identical or different, represent a monovalent hydrocarbon-based group having from 1 to 30 carbon atoms, preferably chosen from the group formed by alkyl groups having from 1 to 8 carbon atoms and aryl groups having from 6 to 12 carbon atoms, and even more preferentially chosen from the group consisting of a methyl, ethyl, propyl, xylyl, tolyl and phenyl group, with the condition according to which the additive X comprises, per molecule, at least two siloxyl units (I.1) bearing epoxyfunctional hydrocarbon-based groups and at least three siloxyl units (I.3) bearing hydrosiloxyl groups. - Y a Z b 1 SiO 4 − a + b 2 - Z 3 2 SiO 1 2 - H d Z e 3 SiO 4 − d + e 2 - Z 2 2 SiO 2 2 in which - a=1 and b=1 or 2 - d=1 and e=1 or 2 - the symbol Y represents a radical comprising a hydrocarbon-based group having from 2 to 20 carbon atoms and an epoxy function, with optionally one or more heteroatoms such as an oxygen atom, preferably the symbol Y is chosen from the radicals consisting of the group: alkyl glycidyl ether, linear, branched or cyclic epoxyalkyl, linear, branched or cyclic epoxyalkenyl and carboxylic acid glycidyl ester, - the symbols Z 1, Z 2 and Z 3, which may be identical or different, represent a monovalent hydrocarbon-based group having from 1 to 30 carbon atoms, preferably chosen from the group formed by alkyl groups having from 1 to 8 carbon atoms and aryl groups having from 6 to 12 carbon atoms, and even more preferentially chosen from the group consisting of a methyl, ethyl, propyl, xylyl, tolyl and phenyl group, with the condition according to which the additive X comprises, per molecule, at least two siloxyl units (I.1) bearing epoxyfunctional hydrocarbon-based groups and at least three siloxyl units (I.3) bearing hydrosiloxyl groups. - a=1 and b=1 or 2 - d=1 and e=1 or 2 - the symbol Y represents a radical comprising a hydrocarbon-based group having from 2 to 20 carbon atoms and an epoxy function, with optionally one or more heteroatoms such as an oxygen atom, preferably the symbol Y is chosen from the radicals consisting of the group: alkyl glycidyl ether, linear, branched or cyclic epoxyalkyl, linear, branched or cyclic epoxyalkenyl and carboxylic acid glycidyl ester, - the symbols Z 1, Z 2 and Z 3, which may be identical or different, represent a monovalent hydrocarbon-based group having from 1 to 30 carbon atoms, preferably chosen from the group formed by alkyl groups having from 1 to 8 carbon atoms and aryl groups having from 6 to 12 carbon atoms, and even more preferentially chosen from the group consisting of a methyl, ethyl, propyl, xylyl, tolyl and phenyl group, with the condition according to which the additive X comprises, per molecule, at least two siloxyl units (I.1) bearing epoxyfunctional hydrocarbon-based groups and at least three siloxyl units (I.3) bearing hydrosiloxyl groups.