It is demonstrated that the catalyst system bis(pentamethylcyclopentadienyl)-zirconium dichloride (Me5Cp)(2)ZrCl2-methylaluminoxane (MAO) is able to produce random copolymers of ethene and l-hexene. The l-hexene incorporation in the copolymers is extremely small. Even in the case of a molar ratio of [ethene] to [1-hexene] of 1/20 in the monomer feed, only 1.4 mol % 1-hexene are incorporated according to C-13 nuclear magnetic resonance (NMR) spectra. Nevertheless, the physical properties of the random copolymers change significantly in this small range of l-hexene incorporation, from a high-density polyethene to a linear low-density polyethene. Thus, the melting temperature, the degree of crystallinity, the density and lamella thickness, and the long period of the alternating crystalline and amorphous regions decrease with increasing I-hexene content in the random copolymers. Blends of high-density polyethene prepared with the system (Me5Cp)(2)ZrCl2-MAO and an elastomeric random copolymer of ethene and l-hexene are phase-separated and show good compatibility, as demonstrated by transmission electron microscopy.