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High modulus polyethylene fibres, both melt and gel-spun, contain the same longitudinal density deficient regions, revealed by permanganic etching, as were found in specimens of the same fibres after treatment by the Leeds high temperature compaction process. For these materials a new model of fibre structure is proposed, which develops as a consequence of nucleation on an extended network of entangled molecules permeating the fibres. Subsequent growth into spaces between the network will encounter stresses due to the contraction on crystallization leading to distributed density deficient regions of high free volume. Each of the four commercial PE fibres examined differs from the others in its characteristic outline and the details of its internal substructure. The structure of commercial polypropylene fibres is also compared.