Abstract The structure of solidification-processed rhenium disilicide is investigated by X-ray diffraction and transmission electron microscopy. It is usually reported to have the tetragonal C11b MoSi2 structure and the stoichiometry of ReSi2. In the present study it is found that rhenium disilicide exhibits an off-stoichiometric Si-deficient composition of Re4Si7. In addition, several structural instabilities are observed by electron microscopy including firstly an orthorhombic distortion of about 0.6% from the tetragonal C11b MoSi2 structure with spot splitting across the {110} twin plane, secondly an incommensuration along the a axis with a periodicity of 1.3nm, thirdly another longer period modulation along the c axis, fourthly a weak monoclinic distortion (β ≈ 90.4°) in some specimens, as revealed by spot splitting in the high-order Laue zone reflections of [100] diffraction patterns, accompanied by twinning on the (001) planes, and fifthly much larger distortions in some [010] patterns plus a chevron structure in the image which may result from a displacive transformation. These structural anomalies are probably related to the stoichiometry of Re4Si7 which may result in a composite modulated structure where the Si sublattice has a larger average periodicity along the a axis than the Re sublattice, as is the case with manganese silicides.