Uniaxially oriented samples of thermotropic random copolyesters of hydroxybenzoic and hydroxynaphthoic acids, and of hydroxybenzoic acid and ethylene terephthalate, have been characterised in detail using wide-angle X-ray diffraction. The technique was used to measure the global chain orientation, and in the case of the first polymer the meridional scattering has been analysed in terms of diffraction from an isolated straight random chain. Optical microstructures were observed between crossed polars, with circularly polarized light and in plane-polarised light with no analyser present. Interpretation of the contrast seen shown that the material is optically biaxial and leads to the conclusion that, in the liquid-crystalline phase, there is long-range correlation of the rotations of the molecules about their chain axes. The polymers are examples of ‘biaxial nematics’. Thermal analysis indicates that the solid phase has a higher level of conformational order than the melt and that the melting range is very broad. Annealing below the melting point leads to the development of localised regions of enhanced order, especially in specimens with a high degree of overall orientation. The combination of electron diffraction and electron microscopy provides evidence that the lateral growth of ordered entities does not necessarily require regular sequences within the otherwise random copolymer molecules. Small crystals based on identical but non-periodic sequences within the molecules are (NPL crystals) proposed as being consistent with the experimental evidence and the implications of a brief statistical analysis.