The double yield point is shown to be a common feature to polyethylene and ethylene copolymers, regardless of the crystallinity level. Particular attention has been paid to the influence of draw temperature and strain rate which unambiguously indicate a combination of two thermally activated rate processes. Various thermal treatments have been investigated in order to check the influence of the crystal thickness distribution and the chain topology on the yield behaviour. Isothermal crystallization at high temperature is shown to have little effect compared with variations of crystallinity, temperature and strain rate in the case of compression-moulded samples. On the other hand, a strong effect has been observed in the case of solution crystallization which is well known to affect the chain-folding topology. The results are fairly consistent with the previous proposal by Takayanagi that (1) two processes govern the plastic deformation of the crystalline lamellae in semi-crystalline polymers, and (2) these processes are closely related to the viscoelastic relaxations in the crystal. The crystalline lamellae may deform plastically through sliding of crystalline blocks (brittle process) and/or homogeneous shear (ductile process). In order to account for the dependency of the brittle-to-ductile transition on the copolymer structure and crystallization method, a molecular model is put forward on the basis of the chain topology concepts borrowed from our former investigations on the tensile drawing and the melting behaviour of ethylene copolymers.