The atomic structures of internal interfaces have recently received considerable attention, not only because of their importance in determining many materials properties, but also because the atomic structure of many interfaces has become accessible to direct atomic-scale observation by modem HREM instruments. In this communication, several interface structures are examined by HREM in terms of their structural periodicities along the interface.It is well known that heterophase boundaries are generally formed by two low-index planes. Often, as is the case in many fcc metal/metal and metal/metal-oxide systems, low energy boundaries form in the cube-on-cube orientation on (111). Since the lattice parameter ratio between the two materials generally is not a rational number, such boundaries are incommensurate. Therefore, even though periodic arrays of misfit dislocations have been observed by TEM techniques for numerous heterophase systems, such interfaces are quasiperiodic on an atomic scale. Interfaces with misfit dislocations are semicoherent, where atomically well-matched regions alternate with regions of misfit. When the misfit is large, misfit localization is often difficult to detect, and direct determination of the atomic structure of the interface from HREM alone, may not be possible.