The invention relates to a rubber mixture for the tread of tyres for motor vehicles. According to the invention, the mixture comprises a matrix rubber and a vulcanised rubber of specific particle size and low hardness. Both rubbers contain carbon black, with the following equation applying: 0 </= X </= Y/3, in which X is the amount of carbon black in the vulcanised rubber and Y is the amount of carbon black in the matrix rubber, both amounts being based on the total amount of the matrix rubber. The resultant tyre has good grip on snow and ice and low wear.