The invention relates to an agent for producing cross-linked polyethylene which contains t-butyl perbenzoate and an alpha -methylstyrene dimer. The invention also relates to a method for producing cross-linked polyethylene according to which polyethylene, t-butyl perbenzoate, an alpha -methylstyrene dimer and possibly additives are mixed, and the resulting mixture is extruded and directly afterwards cross-linked at a high temperature. The invention further relates to the use of said agent for producing cross-linked polyethylene.