Polyethylene containing trans- or cis-vinylene units in the main chain has been synthesized by means of partial hydrogenation of trans- or cis-polypentenamer (TP or CP), and trans-polyoctenamer (TO). Crystalline structure of the polymers has been investigated with wide-angle X-ray diffraction, FT-IR analyses, solid-state NMR measurements and quantum chemical calculations of the NMR chemical shifts. These results clear that the partially hydrogenated TP or CP samples having an average number of methylene units of 6.9-8.4 per vinylene unit forms not only orthorhombic crystal but hexagonal-like crystal. (C) 2011 Elsevier Ltd. All rights reserved.