We investigate the exciton states at the interface of organic and inor
ganic quantum wells (QW) when the energy of the 2D Frenkel exciton in
the organic QW is near that of the 2D Wannier exciton in the inorganic
semiconductor QW. The dipole-dipole resonance interaction is responsi
ble for the appearance of new states: mixed Frenkel-Wannier excitons w
ith unusual properties such as large oscillator strengths, typical of
Frenkel excitons and can also have large exciton radii, typical for Wa
nnier-Mott excitons. The dispersion curves display a minimum away from
the center of the Brillouin zone, which is expected to influence the
optical properties. The characteristics of organic and inorganic cryst
als required to obtain appropriate materials for studying hybrid state
s are discussed. Some illustrative calculations are performed for an o
rganic layer deposited on a ZnCdSe quantum wells.