The true stress-strain characterization of the tensile yield as a function of temperature and cross-head speed is reported for three ethylene-butene copolymers having different crystal weight fractions in the range 0.66-0.35. Evidence is given of two plastic processes operating competitively depending on the experimental conditions. Crystal shear and crystal block sliding are suggested on the basis of the concept of the mosaic block structure of the crystalline lamellae. Small-angle and wide-angle diffraction measurements together with infrared measurements support this conclusion. Two theoretical models of plastic deformation borrowed from solid state physics are proposed to account for our findings. These are a homogeneous crystal slip involving thermal nucleation of dislocations and a heterogeneous crystal slip operating through the defective block boundaries. The competitive action of the two processes which relies on the requirement of the lower energy-consuming pathway of deformation is discussed in terms of a combination between thermal activation and strain-hardening. The proposed models provide an explanation for the major influence of the crystal thickness on the temperature of occurrence of the homogeneous slip. The role of the amorphous phase is discussed in relation to the strain-hardening accompanying the two processes.