The thermal behaviour and morphology of series of homogeneous ethylene-propylene and ethylene-l-butene copolymers, which cover wide ranges in comonomer content, are studied by differential scanning calorimetry (DSC), time-resolved small-angle X-ray scattering (SAXS), wide-angle X-ray diffraction (WAXD) and transmission electron microscopy (TEM). The thermal behaviour and the morphology of the copolymers change in a continuous way as the comonomer content is increased, supporting the model in which the morphology changes gradually from a lamellar base morphology into a granular one consisting of small block-shaped structures. When the comonomer amount is raised further to very high contents, possibly via fringed-micelles a morphology consisting of loosely packed ethylene sequences is obtained. Although the granular structures, present in the very-low-density copolymers, are too small and/or too imperfect to be detected by WAXD, the crystallisation and melting processes could still be readily measured by DSC and SAXS. Real-time SAXS measurements during a scan-iso temperature-time heating program, as used in some temperature-modulated DSC (TMDSC) measurements, shows that in a homogeneous ethylene-l-butene copolymer (6.4 mole% l-butene) considerable instantaneous structural changes occur during dynamic (heating) and static (isothermal) measurements, as is, for instance, reflected in the significant increase of the SAXS invariant during the short isothermal stays. (C) 2000 Elsevier Science Ltd. All rights reserved.