The present invention concerns a polymer composition and films manufactured from such compositions. The present polymer compositions comprise 80-99 wt-% on an essentially linear polyethylene with a component having a relatively low MW and a relatively high density, and another component having a relatively high MW and a relatively low density, said linear polyethylene having an MFR21 of at least 5 g/10 min, a maximum MFR2 of 6 g/10 min, a density of 915-945 kg/m3. Further the compositions contain 1-20 wt-% of a branched copolymer of ethylene and an acrylate monomer with 20-28 wt-% acrylate monomer units. The MFR2 of the copolymer is 0.4 to 2.0 g/10 min. Cross-laminated film materials having good mechanical properties can be manufactured from the present compositions.