An elastomeric composition includes at least one diene elastomeric polymer, at least one salt or oxide of a transition metal belonging to groups IIIA, IVA, VA, VIA, VIIA, or VIIIA of the Periodic Table, at least one vulcanization accelerator, sulphur or derivatives thereof, and at least one reinforcing filler. The elastomeric composition is substantially free of zinc or derivatives thereof. A tire for a vehicle wheel including at least one component including the elastomeric composition and a tread band for a tire including the elastomeric composition are also disclosed. The at least one diene elastomeric polymer may include a glass transition temperature lower than 20° C. The at least one salt of a transition metal may be an organic or inorganic metal salt. The at least one oxide of a transition metal may include one or more of: cobalt oxide; cerium oxide; molybdenum oxide; manganese oxide; and iron oxide.