Some theoretical models, including lamellar distortions of the second kind, are described. To test the influence of lamellar distortions on the small-angle X-ray scattering (SAXS) of polymers, some theoretical patterns were calculated with different values of the model parameters. SAXS diffraction profiles were recorded for three commercial copolymer samples of linear low-density polyethylene containing different comonomers and one commercial homopolymer sample of high-density polyethylene; these were successively analyzed by a fit to the calculated profiles corresponding to our theoretical models. Transmission electron microscopy images were obtained of the lamellar morphologies of the four samples. From these, we concluded that the homopolymer sample displayed excellent organization on lamellar stacks, whereas the copolymer samples showed more imperfect lamellar morphologies, so it was useful, in the latter case, to introduce a distorted lamellar structure in calculated SAXS diffraction patterns. By use of wide-angle X-ray scattering, we also determined the overall crystallinities of the samples. (C) 2003 Wiley Periodicals, Inc.