Silica-containing rubber mixture produced from at least one rubber, from a sulphur-containing alkoxysilane, from a crosslinking agent, from a filler, and optionally from further rubber auxiliaries, characterized in that the said mixture comprises from 0.1 to 15 parts by weight, based on 100 parts by weight of rubber used, of a silicon-free polysulphide additive of the formula A-S- x -S-Y-S- x -S-A where x is 0, 1 or 2, Y is an optionally substituted or heteroatom-containing aliphatic, cycloaliphatic or aromatic group and A is a moiety where R 2 to R 2 are identical or different and are hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or a group -CH 2 -OR 5, -CH 2 -CH 2 -OR 5, -NHR 5, -COR 5, - COOR 5, -CH 2 COOR 5, where R 5 = hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or C 1 -C 6 -acyl, or A is a moiety in which R 1 and R 2 are identical or different and are hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or a group -CH 2 -OR 5, -CH 2 -CH 2 -OR 5, -NHR 5, -COR 5, -COOR 5, -CH 2 COOR 5, where R 5 = hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloal kyl, C 6 -C 10 -aryl or C 1 -C 6 -acyl, or A is a moiety in which R 1 to R 2 are identical or different and are hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or a group -CH 2 -OR 5, -CH 2 -CH 2 -OR 5, -NHR 5, -COR 5, -COOR 5, -CH 2 COOR 5, where R 5 = hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or C 1 -C 6 -acyl, and R 6 is hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or a group -CH 2 -OR 5, -CH 2 -CH 2 -OR 5, -NHR 5, COR 5, -COOR 5, -CH 2 COOR 5, where R 5 = hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or C 1 -C 6 -acyl and y is 0, 1 or 2, or, if Y is -(CH 2) 6 - and x is 0, A is in which R 8 and R 9 are mutually independently hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or a group - CH 2 -OR 5, -CH 2 -CH 2 -OR 5, -CH 2 -COOR 5 -CH 2 -CH 2 -COOR 5, and R 8 and R 9 can optionally together with the respective nitrogen atom form a ring and R 5 is as defined above and at least one of the moieties R 8 and R 9 comprises one or more oxygen atoms. Y is an optionally substituted or heteroatom-containing aliphatic, cycloaliphatic or aromatic group and A is a moiety where R 2 to R 2 are identical or different and are hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or a group -CH 2 -OR 5, -CH 2 -CH 2 -OR 5, -NHR 5, -COR 5, - COOR 5, -CH 2 COOR 5, where R 5 = hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or C 1 -C 6 -acyl, or A is a moiety in which R 1 and R 2 are identical or different and are hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or a group -CH 2 -OR 5, -CH 2 -CH 2 -OR 5, -NHR 5, -COR 5, -COOR 5, -CH 2 COOR 5, where R 5 = hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloal kyl, C 6 -C 10 -aryl or C 1 -C 6 -acyl, or A is a moiety in which R 1 to R 2 are identical or different and are hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or a group -CH 2 -OR 5, -CH 2 -CH 2 -OR 5, -NHR 5, -COR 5, -COOR 5, -CH 2 COOR 5, where R 5 = hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or C 1 -C 6 -acyl, and R 6 is hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or a group -CH 2 -OR 5, -CH 2 -CH 2 -OR 5, -NHR 5, COR 5, -COOR 5, -CH 2 COOR 5, where R 5 = hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or C 1 -C 6 -acyl and y is 0, 1 or 2, or, if Y is -(CH 2) 6 - and x is 0, A is in which R 8 and R 9 are mutually independently hydrogen, C 1 -C 6 -alkyl, C 5 -C 6 -cycloalkyl, C 6 -C 10 -aryl or a group - CH 2 -OR 5, -CH 2 -CH 2 -OR 5, -CH 2 -COOR 5 -CH 2 -CH 2 -COOR 5, and R 8 and R 9 can optionally together with the respective nitrogen atom form a ring and R 5 is as defined above and at least one of the moieties R 8 and R 9 comprises one or more oxygen atoms.