The invention relates to a composition that comprises a thermoplastic or elastomeric polymeric substrate (A) and an antistatic mixture (B) in the form of contiguous fibers, which mixture comprises (b1) an organic polymeric material that is fibrous or forms fibers on mixing and is not soluble in the thermoplastic or elastomeric polymeric substrate (A); (b2) a polymer or copolymer capable of ion conduction that has blocks for complexing or solvating a salt of an inorganic or low-molecular-weight organic protonic acid (b3) and has a better compatibility with the organic polymer (b1) that is fibrous or forms fibers on mixing than with the polymeric organic substrate (A); and (b3) a salt of an inorganic or low-molecular-weight organic protonic acid such as NaClO.sub.4 or K P F.sub.6 that has been complexed or solvated in the polymer or copolymer (b2). The invention relates also to the antistatic mixture (B) as such, to its use in rendering polymers antistatic and to a process for the preparation of antistatic thermoplastic or elastomeric polymeric substrates.