Abstract: It is well known that the spectra of periodic differential operators consist of bands separated in the general case by lacunas. The bands in the spectrum are the images of the dispersions laws. The general theory of periodic differential operators does not exclude the situation when the extrema of the dispresion laws are attained inside Brillouin zone. At the same time, in all known examples the extrema were attained either at the boundary of the Brillouin zone or in its center. We cover such lack of the examples and construct a wide class of differential periodic operators in Euclidean domain, whose dispersion laws attain extrema in almost arbitrary internal points of the Brillouin zone.