a rubber composition containing a bismaleimide compound represented by the general formula ## str1 ## wherein r is a divalent acyclic aliphatic group , cyclic aliphatic group , aromatic group , or alkylaromatic group , these groups optionally containing a hetero atom selected from o , n and s in their chain or side substituent , a sulfenamide compound represented by the general formula ## str2 ## wherein r 1 and r 2 denote independently from each other a hydrogen atom , an acyclic aliphatic group , or cyclic aliphatic group , or r 1 and r 2 together denote a chain aliphatic group which optionally contains an oxygen atom , provided that r 1 and r 2 cannot simultaneously denote a hydrogen atom , a dithiophosphoric acid compound represented by the general formula ## str3 ## wherein r 3 and r 4 denote each an aliphatic group , and sulfur ; or a bismaleimide compound represented by the general formula defined above , an aromatic carboxylic acid anhydride , sulfur and / or a sulfur donor , and volcanization accelerators .