The phase structure of three linear polyethylene (PE) samples, crystallized from the melt at high pressure, has been studied by electron microscopy and high-resolution solid-state C-13 n.m.r. spectroscopy. In general, three phases are required to account for the n.m.r. data : the lamellar crystalline phase, the crystalline-amorphous interphase and the amorphous phase. All three are present in high-molecular-weight samples but there is no amorphous phase for samples with lower molecular weights and large lamellar thicknesses. The amorphous phase appears when the ratio of the number-averaged extended molecular chain length (X(n)) to the number-averaged crystalline stem length (L(n)) exceeds two. High-pressure-crystallized materials differ from those crystallized at atmospheric pressure in that the mass fraction of the amorphous phase does not exceed 0.05; the thickness of the crystalline-amorphous interphase reaches 8.0 nm for material with the highest molecular weight, a value which is considerably larger than those reported for samples crystallized at atmospheric pressure or which have been estimated theoretically. Extraordinarily long C-13 spin-lattice relaxation times have been found : a figure of T1C = 7000 s, higher than any previously reported, for the highest-molecular-weight sample is still less than would be expected from the large lamellar thickness. In consequence, this relaxation is attributed to molecular motion in the vicinity of the crystal defects; this is in addition to C-13 spin diffusion to the non-crystalline region, occurring with a shorter T1C. The discrepancy between the observed and calculated values of T1C increases as the molecular weight falls in those samples for which the crystal stem lengths exceed the extended molecular lengths. For these, the unexpectedly shorter T1C is attributed to defects such as methyl end-groups within the crystalline regions.