  An analysis of Luttinger's theorem shows that -- contrary to recent claims --
it is not valid for a generic Mott insulator. For a two-orbital Hubbard model
with two electrons per site the crossover from a non-magnetic correlated
insulating phase (Mott or Kondo insulator) to a band insulator is investigated.
Mott insulating phases are characterized by poles of the self-energy and
corresponding zeros in the Greens functions defining a ``Luttinger surface''
which is absent for band insulators. Nevertheless, the ground states of such
insulators with two electrons per unit cell are adiabatically connected.
