When polyethylene (PE) is deformed to large strains, the stress originates from both the viscous forces associated with the plastic deformation of the crystallites by slip and fragmentation processes and the entropic elastic forces arising from the stretching of the entangled amorphous regions, Relative weights of the different processes change with the crystallinity. The dependencies were analyzed in a comprehensive study on a series of samples encompassing a large range of crystallinities: PE, low-density PE (LDPE), and ethylene-vinylacetate copolymers. The comparison was based on measured true stress-strain curves for constant strain rates. For the samples with higher crystallinity, which show a necking, this was achieved by employing a video-controlled tensile testing machine. Recovery properties of the sample were studied in step-cycle runs, where the load was applied stepwise and interrupted after each step by an unloading-reloading loop. Simultaneous with the mechanical testing, the related texture changes were determined by a measurement of the WAXS patterns. In spite of the large changes in the gross mechanical properties from solid- to rubberlike, there exists a common general scheme for the deformation behavior. For all samples, one finds four characteristic points where the differential compliance changes. They may be associated with (1) the onset of isolated slip processes, (2) a change into a collective activity of the slips, (3) the beginning of crystallite fragmentation, and (4) chain disentanglement resulting in a finite truly irreversible deformation. When the crystallinity is increased, the stresses at the four transition points also increase. The related strains, however, remain essentially constant. Crystal textures are also a function of the imposed strain only, the dependencies being common for all samples. Experiments support the novel picture of a granular substructure of the crystalline lamellae as a basic structural feature. Block slips with the three surfaces as slip planes enable the system to easily react on each imposed strain in a well-defined way.