A vulcanizable rubber composition is described comprising a cross-linkable unsaturated chain polymer base including natural rubber, at least a copolymer obtainable by polymerizing a conjugated diolefin with a vinyl aromatic hydrocarbon, and a main carbon black-based reinforcing filler, wherein
a) the copolymer is obtainable by polymerizing in 1,2 form with the vinyl aromatic hydrocarbon at least 50% by weight of the conjugated diolefin, so as to obtain in the copolymer a quantity of from 30% to 70% by weight to the total weight of the same of an olefin fraction having a 1,2 structure, and
b) the carbon black has a DBP absorption value measured according to ISO 4656-1 equal to at least 110 ml/100 g, a reduction in the DBP absorption value measured after compression according to ISO 6894 equal to at least 25 ml/100 g and a surface area measured by means of CTAB absorption according to ISO 6810 not greater than 120 m.sup.2 /g.