The experimental study of relaxation of anion and cation excitons at the selective VUV-(valence) and soft X-ray (inner-shell) excitations for binary BeO crystal and multicomponent oxide crystals Be2SiO4, Al2Be3Si6O18 and Y2SiO5 is presented. Results show that the relaxation during the time-scale of decay of short-living anion and cation excitations leads to creation of self-trapped excitons at the corresponding low-symmetry (tetrahedral) local structural units of crystalline lattice. This can be caused by increase of dynamical instability of such a local structural units (in comparison with high symmetry ones), which facilitates self-trapping processes in these systems.