A rubber composition which is free of precursor of at least one carcinogenic nitrosamine, is capable of vulcanization at a temperature of between 95° C. and 140° C., and has a vulcanization system which includes: a) sulfur; b) an accelerator compound; c) an ultra-accelerator compound; d) a vulcanization amine activator. A process for vulcanizing this composition in the manufacture of a new tire or in the repair and/or recapping of a worn tire.