A single-component high-temperature-curing reactive composition based on natural and/or synthetic elastomers having olefinic double bonds and on vulcanizing agents is provided. Such compositions contain at least one liquid polyene with a molecular weight between 400 and 80,000, preferably between 800 and 25,000; at least one block copolymer with at least one polyene block and at least one saturated block; and a vulcanizing system of sulfur and accelerators and/or quinone oximes, if applicable. Such high-temperature-curing reactive compositions are useful as single-component adhesives, sealant or coating compositions or sealing compounds in automobile body manufacture.