The structure of rigid-chain polyesters and polyamides which possess flexible side chains consisting of methylene or 1,4,7-trioxaoctyl oxide units have been investigated by means of X-ray scattering. The X-ray studies were performed on fibres and monodomains. Additional information was gained from calorimetric, dilatometric and microscopic studies. The investigations revealed that these polymers display mesophases and that the structures of the mesophases differ from those observed for discotic and calamitic phases. They are characterized by the fact that in the ordered and disordered phases board-like molecules are stacked parallel on top of each other and that these stacks of molecules are oriented parallel to each other. In the least ordered phase the molecules are only oriented parallel to each other. The various modifications of the mesophases observed so far differ with respect to each other in terms of the order within the stacks as well as in terms of the spatial arrangements of the stacks. A characteristic feature is the frequent absence of any correlation between the long range order which exists along different principal axes of the structure. We have coined the term sanidic for this new type of mesophase.