It is stated that an electron can be in a state localized at an intercrystallite or twin boundary or stacking fault irrespective of the specific structure of the transition region. It is important that the crystal containing such a boundary must be non-periodic “as a whole.” The one-dimensional model (two abutting Kronig–Penney lattices for which the spectrum of localized states is determined) is considered. The bands containing one or two discrete levels alternate in a complex way in the spectrum. ©1998 American Institute of Physics.