Electronic spectra of the Xe2 molecules in the energy range of 77700-89300 cm ^-1 are recorded. The method of resonance enhanced multiphoton ionization of molecules in a supersonic molecular beam was used, in which excitation of the molecules by three photons was followed by ionization caused by a fourth photon (the (3+1) REMPI method). Analysis of the vibrational structure of observed systems of bands yielded information about the dissociation energy and the molecular constants for ungerade states of Xe*2 molecules. On the basis of the Franck-Condon principle, the equilibrium distances for potential curves were estimated from the relative intensities in vibrational progressions. Data on 16 new electronic states of diatomic xenon molecules with the dissociation limits Xe* ₂ → ^{6 1} (5p S ₀) +Xe* (5p ⁵ 6p,5d,7s,7p) were obtained.