Process for the preparation of diene polymers or random vinyl arene-diene copolymers which comprises (co)polymerizing, anionically, in the presence of at least one hydrocarbon solvent, at least one conjugated diene monomer and optionally at least one vinyl arene, in the presence of at least one lithium-based initiator, at least one aprotic polar compound, and at least one compound containing one or more functional groups of the acetylenic type. Said process allows diene polymers or random vinyl arene-diene copolymers to be obtained, which can be advantageously used in the production of tires, in particular in the production of tire treads. The diene polymers or the random vinyl arene-diene copolymers obtained through said process can also be used for the modification of plastic materials [for example, for obtaining high impact polystyrene (HIPS)].