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We present the results of low-temperature scanning tunneling microscopy and scanning tunneling spectroscopy investigations of the spatial oscillations of the local electron density of states on clean Ge(111)2x1 surfaces. The oscillations appear in the vicinity of the boundaries between domains with di®erent atomic arrangements. We introduce a tight-binding based model, which consistently explains the observed experimental features in terms of the formation of two-dimensional surface states within the surface band gap due to the breaking of the translational symmetry at the domain boundaries.