Abstract: Eight kinds of nonclasslcal periodic lattices with locally 8-fold rotational symmetries are introduced.They can be described via nonclassical Planc-crystallographic groups. The periodic lattices may be interpreted by the projections on the plane of the corresponding unit cells consisting of embedding polyhedrons, respectively. The Fourier-transform patterns of the Periodic lattices have striking approximate "8-fold rotational symmetries", some of which are similar to those displaying in the electrton-diffraction patterns of so-called quasicrystals.