A vulcanizable rubber composition suitable for the production of rubber materials having improved scorching stability and heat aging resistance can be obtained by compounding raw material rubber with a sulfenamide compound having the following general formula ##EQU1## wherein X represents a residue selected from the group consisting of residues of hydrocarbon, alkyl ether and secondary alcohol having 2-20 carbon atoms, and residues represented by the general formulae ##EQU2## (wherein R' represents a residue of hydrocarbon or alkyl ether having 0-20 carbon atoms, and R" represents a hydrocarbon residue having 1-10 carbon atoms), and R.sub.1, R.sub.2, R.sub.3 and R.sub.4 are same or different and are selected from hydrocarbon residues having 2-10 carbon atoms, and hydrogen atom, or R.sub.1 is ringed with R.sub.2 and/or R.sub.3 is ringed with R.sub.4, through the nitrogen atom of the general formula (1), to form heterocyclic rings of 5-7 members.