**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.