The invention produces suspensions of higher α-olefins without using cryogenic comminution as well as without using polymer precipitation by adding a non-solvent to a polymer solution. Fine polymer dispersions are produced by thermal re-precipitation of a polymer in a liquid being a non-solvent for that polymer at room temperature and being capable of dissolving the polymer at a higher temperature. The polymer component of a suspension is produced by co-polymerization of higher α-olefins in a monomer mass in the presence of a Ziegler-Natta catalyst.