Linear low and high density polyethylene sheets were compression molded and crystallized at a 5-10 degreesC/min cooling rate. Parts of the sheets were annealed at different temperatures up to 2 degreesC below the melting temperature. The small angle X-ray scattering (SAXS) and the wide angle X-ray scattering intensities of the annealed samples were studied. SAXS intensities showed particle scattering with a bimodal size distribution. The estimated radii of gyration were 15-17 nm and 5-7 nm, respectively. The crystallinity and the radius of gyration increased slightly with increasing annealing temperature for some samples, others did not show any change. No peaks characteristic of intercorrelated lamellar crystallinity in the SAXS intensities developed during the annealing. The original broad peak of high density polyethylene disappeared from the SAXS recordings on annealing. The length of the perfect chain versus melting temperature was calculated by the Thomson-Gibbs formula and Flory's concept of melting temperature depression where methyl groups and tertiary carbon atoms at the branches were regarded as second components (solvent). Linear relationships were found for both cases. Experimental data for a linear low density polyethylene obtained from the literature were in between the two functions. A lamellar model of crystallization corresponding to the data is proposed.