In cold-drawn, necked high-density polyethylene, solid-state nuclear magnetic resonance (NMR) has identified a major fraction of chain segments intermediate to the ordered crystalline and the almost isotropic amorphous phases. This partially mobile and disordered all-trans fraction in the strain-hardened sample contains 38 +/- 6% of all chain segments in the bulk. Thus, it represents the second largest component in the system, ahead of the disordered gauche-containing or amorphous (17 +/- 4%) and the monoclinic crystalline (4 +/- 2%) phases. A series of one- and two-dimensional NMR experiments, several of which make use of an "inverse C-13 T-1 relaxation time filter" for selective observation of the intermediate-component signals, show the intermediate component (or components) to consist of all-trans chains with disordered packing. While the crystalline component has a standard deviation of the chain axis from the draw direction of 1 degrees, the intermediate components exhibit an similar to 8 degrees spread of chain-axis orientations from the draw axis. The chains in the intermediate components undergo fast rotational motions around their axes, with motional amplitudes of ca. 20 degrees.