The plastic behaviour of polyethylene and ethylene copolymers is studied under uniaxial tensile testing with particular attention to the development of plastic instability. Heterogeneous crystal slip is suggested to take place when homogeneous crystal slip either is not allowed at the temperature and strain rate of the experiment or is exhausted owing to extension of the chain folds. The chain unfolding concomitant to the fragmentation of the crystalline lamellae is suspected to have a low strain hardening that is responsible for the phenomenon. Partial screw dislocations with a shorter Burgers vector than in the case of homogeneous slip are proposed to become operative because of the activation of 90 degrees chain twists in the crystalline stems. Dissociation of dislocations into partials involves stacking faults in the orthorhombic structure that may turn into monoclinic structure through a martensitic-like transformation. Crystal slip is likely to concentrate in these faulty regions owing to the reduced molecular interactions and lower density. Two types of correspondence of the transformed monoclinic phase with the parent orthorhombic structure are observed. The modification of the chain-folding macroconformation as a function of the crystallinity of the materials is suspected to influence the transformation shear mode.