The influence of the topology of the amorphous phase on deformation instabilities, leading to kinking and to fragmentation of lamellae is discussed. Samples of polyethylene of diverse structure were deformed in the planestrain compression. The accompanying structural changes were analyzed using DSC, WAXS and SAXS. Several deformation instabilities occur at various true strains. At e = 0.3-0.4 lamellae oriented specifically along the loading direction undergo microbuckling instability, leading to cooperative kinking. This transition manifests as the second macroscopic yield. For a given layers stiffness the microbuckling depends on the ratio of the amorphous and crystalline thickness. At e = 0.6-1.0 the lamellae fragmentation due to the localization of crystallographic slip was observed, relatively weak at e = 0.6, but extensive at e = 1. Fragmentation is initiated by stress concentrations at the crystal-amorphous interface due to stretched 'stress transmitter' chains ST. Consequently, the critical strain of fragmentation depends inversely on the ST fraction at the interface - when it is low the stress concentrations grow stronger, prompting an earlier slip localization and subsequent lamellae fragmentation. Extensive fragmentation reduces deformation constraints and allows the formation of a new crystal ordering along the flow direction.