Dimorphic fibres in angiosperm woods are designated when zones of two different kinds of fibres can be distinguished in transverse sections. The usage of most authors contrasts wider, thinner-walled, shorter (sometimes storied) fibres with narrower, thicker-walled fibres that have narrower lumina. The wider fibres can be distinguished in longitudinal sections from axial parenchyma, which usually consists of strands of two or more cells each surrounded by secondary walls (and thus different from septate fibres). This phenomenon occurs in some Araliaceae, Asteraceae, Fabaceae, Myrtales (notably Lythraceae), Sapindales (especially Sapindaceae), Urticales and even some Gnetales. Additional instances can doubtless be found, especially if instances of wide latewood fibres together with narrow earlywood fibres are included. There is little physiological evidence on differential functions of dimorphic fibres, except in Acer, in which hydrolysis of starch in the wide fibres is known to result in transfer of sugar into vessels early in the growing season. Starch storage in axial parenchyma may, in a complementary way, serve for embolism reversal and prevention and thus for maintenance of the water columns. Crystalliferous fibres (Myrtales, Sapindales) can be considered a form of fibre dimorphism that deters predation. Gelatinous fibres, often equated with tension wood, can also be considered as a form of fibre dimorphism. The evolutionary significance of fibre dimorphism is that a few small changes in fibre structure can result in the accomplishment of diversified functions. © 2013 The Linnean Society of London, Botanical Journal of the Linnean Society, 2014, 174, 44–67.