The local symmetry of dislocation centers in CdS crystals was studied by piezospectroscopy of space resolved photoluminescence of individual screw dislocations. The limited set of dislocationCscenters (2 from a total of 6) was found to be characteristic for each screw dislocation and that set determines the asymmetry of the core structure. The space‐ and time‐nonstationarity of the dislocation domains observed in the polarized emission of dislocations are explained by the reorientation of one‐dimensionally orderedCscenters in the core of the screw dislocation gliding by the Peierls mechanism.