The most important symmetry properties of the incommensuratelymodulated crystal structures are investigated by use of exactsymmetry theory of quasi-one-dimensional systems in the framework ofgroup theory. It is shown that typical characteristic formulaedeveloped for the description of scattering cross sections ofone-dimensionally modulated crystals can be directly derived by theline-group technique. A symmetry analysis of static solitonstructures is performed, representing a new method for theinvestigation of elementary excitations of crystals modulatedincommensurately. It leads to the description of symmetry breaking,to the selection rules and hints at the similarity of symmetrybehaviour of static and dynamic solitons. The actual formulae forDebye-Waller factors in the case of incommensurately modulatedcrystals are calculated and tabulated by using generating elementsof the line groups concerned.