[en] The object of this thesis is an experimental study of a novel quasi-crystalline state of certain materials. The structure in such a state is characterized by a three-dimensionally periodic basic structure which is deformed by a static displacement wave. The peculiarity of the structure is marked by the incommensurability of the displacement wave with respect to the basic lattice, resulting in a loss of three-dimensional periodicity. The wave-length and the amplitude of the modulation wave are temperature dependent. Upon raising the temperature the latter vanishes: a phase transition occurs to a normal crystalline state. In order to see what exactly happens at the phase transition, extensive neutron scattering experiments have been performed. This technique offers the opportunity to determine both the spatial arrangemet of the atoms as well as the time dependence of the atomic displacements. Dielectric measurements have been done to study the coupling of the modulation wave with an external electric field. For a similar reason ultra-sonic measurements have been performed, where the response of the sample to an external stress is measured. Finally, the nuclear quadrupole resonance technique was employed to investigate the electric field gradient at a specific type of nucleus. The latter three techniques were employed in the study of Rb₂ZnBr₄, since good single crystals with a volume of a few cm³ were available of this compound, whereas only small crystals (.1 cm³) of Na₂CO₃ were available. (Auth.)