The invention relates to a novel block copolymer comprising at least one polymeric monoalkenyl arene block and at least one polymeric myrcene block having a low and stable viscosity and having good adhesive properties when used in an adhesive composition or as a damping material. An adhesive composition is also described, preferably containing an SMS triblock optionally mixed with an SM diblock. The adhesive composition comprises: 1) a block copolymer having at least one polymeric monoalkenyl arene block and at least one polymeric myrcene block; 2) a tackifier; 3) optional plasticizer; and 4) optionally a stabilizer. Compared with adhesive compositions comprising SIS block copolymers, those comprising SMS block copolymers have lower and more stable viscosity.