Elementary energy bands in solids are defined generalizing the notion of si
mple and composite energy bands. All energy branches of elementary energy b
ands are connected. Following the connectivity of the energy branches in el
ementary energy bands, a new notion of unavoidable degeneracy is establishe
d, for which the crossings can be moved but not removed. This degeneracy do
es not depend on the particular shape of the potential and is present in al
l crystals of some given space group symmetry.