Sulfur-crosslinkable rubber mixture, characterized in that it comprises at least the following constituents: - at least one filler and - 10 to 100 phr of at least one polymer A of the following formula I): where S is a sulfur atom, and P is a polymer chain which is obtainable by anionic polymerization of at least one conjugated diene and optionally one or more vinylaromatic compounds and which has optionally been chain end-modified, R 1 is independently selected from C 1 -C 11 -alkyl, C 6 -C 11 -aryl, C- 7 -C 11 -aralkyl and C 2 -C 11 -dialkyl ether, preferably C 1 -C 11 -alkyl, more preferably C 1 -C 8 -alkyl, R 2 is independently selected from H, C 1 -C 11 -alkyl, C 6 -C 11 -aryl, C 7 -C 11 -aralkyl, C 2 -C 11 -dialkyl ether and -SiR 3 R 4 R 5 in which R 3, R 4 and R 5 are independently selected from H, C 1 -C 16 -alkyl, C 6 -C 16 -aryl and C 7 -C 16 -aralkyl, and R 2 is preferably independently selected from H and -SiR 3 R 4 R 5 in which R 3, R 4 and R 5 are independently selected from H, C 1 -C 16 -alkyl, C 6 -C 16 -aryl and C 7 -C 16 -aralkyl, and n is an integer selected from 1 to 200, preferably 1 to 100, more preferably 1 to 50, where the -S-R 1 -S-R 2 group (s) are bonded to the backbone of the polymer chain P. - at least one filler and - 10 to 100 phr of at least one polymer A of the following formula I): where S is a sulfur atom, and P is a polymer chain which is obtainable by anionic polymerization of at least one conjugated diene and optionally one or more vinylaromatic compounds and which has optionally been chain end-modified, R 1 is independently selected from C 1 -C 11 -alkyl, C 6 -C 11 -aryl, C- 7 -C 11 -aralkyl and C 2 -C 11 -dialkyl ether, preferably C 1 -C 11 -alkyl, more preferably C 1 -C 8 -alkyl, R 2 is independently selected from H, C 1 -C 11 -alkyl, C 6 -C 11 -aryl, C 7 -C 11 -aralkyl, C 2 -C 11 -dialkyl ether and -SiR 3 R 4 R 5 in which R 3, R 4 and R 5 are independently selected from H, C 1 -C 16 -alkyl, C 6 -C 16 -aryl and C 7 -C 16 -aralkyl, and R 2 is preferably independently selected from H and -SiR 3 R 4 R 5 in which R 3, R 4 and R 5 are independently selected from H, C 1 -C 16 -alkyl, C 6 -C 16 -aryl and C 7 -C 16 -aralkyl, and n is an integer selected from 1 to 200, preferably 1 to 100, more preferably 1 to 50, where the -S-R 1 -S-R 2 group (s) are bonded to the backbone of the polymer chain P. S is a sulfur atom, and P is a polymer chain which is obtainable by anionic polymerization of at least one conjugated diene and optionally one or more vinylaromatic compounds and which has optionally been chain end-modified, R 1 is independently selected from C 1 -C 11 -alkyl, C 6 -C 11 -aryl, C- 7 -C 11 -aralkyl and C 2 -C 11 -dialkyl ether, preferably C 1 -C 11 -alkyl, more preferably C 1 -C 8 -alkyl, R 2 is independently selected from H, C 1 -C 11 -alkyl, C 6 -C 11 -aryl, C 7 -C 11 -aralkyl, C 2 -C 11 -dialkyl ether and -SiR 3 R 4 R 5 in which R 3, R 4 and R 5 are independently selected from H, C 1 -C 16 -alkyl, C 6 -C 16 -aryl and C 7 -C 16 -aralkyl, and R 2 is preferably independently selected from H and -SiR 3 R 4 R 5 in which R 3, R 4 and R 5 are independently selected from H, C 1 -C 16 -alkyl, C 6 -C 16 -aryl and C 7 -C 16 -aralkyl, and n is an integer selected from 1 to 200, preferably 1 to 100, more preferably 1 to 50, where the -S-R 1 -S-R 2 group (s) are bonded to the backbone of the polymer chain P.