A curable low sulfur liquid rubber composition including at least one polymer which contains, in polymerized form, at least one monomer having a carbon chain of four and a peroxide system which includes at least one organic peroxide and at least one coagent. The polymer has a vinyl content of 1% to 90% and a number average molecular weight of 800 g/mol to 70,000 g/mol. The curable low sulfur liquid rubber composition has a sulfur content of 0 to 1%, by weight, and is curable at a temperature of 100° C. to 190° C.