  Starting from the tight-binding dielectric matrix in the random phase
approximation we examine the collective modes and electron-hole excitations in
a two-band electronic system. For long wavelengths (${\bf q}\rightarrow0$), for
which most of the analysis is carried out, the properties of the collective
modes are closely related to the symmetry of the atomic orbitals involved in
the tight-binding states. In insulators there are only inter-band charge
oscillations. If atomic dipolar transitions are allowed, the corresponding
collective modes reduce in the asymptotic limit of vanishing bandwidths to
Frenkel excitons for an atomic insulator with weak on-site interactions. The
finite bandwidths renormalize the dispersion of these modes and introduce a
continuum of incoherent inter-band electron-hole excitations. The possible
Landau damping of collective modes due to the presence of this continuum is
discussed in detail.
