VIbrational wavefunctions are calculated for a number of electronically excited states of molecular oxygen whose potential curves are obtained by large-scale confiiuration interaction calculations. The calculated oscillator strengths for the transitions to the first eleven vibrational levels corresponding to the discrete portion of the Schumann-Runge band system arc in quite good agreement with esperimental data. The theoretical crossing of the 3rlu, 'flu and 5flu potential curves leading to predissociation of 02 in its 3ZG state is also determined. The three relatively strong hitherto unidentifitd bands at the high-energy side of the Schumann-Runge continuum at 9.96,10.28 and 10.58 eV respectively are shown to result from transitions to the fist three vibrational levels of a second mixed valence-Rydbeg state of 3ZG symmetry determined earlier, calculated at 9.93, 10.29 and 10.63 eV respectively; the obscrvedfvalues for these lines cannot be explained in the usual way on the basis of Franck-Condon overlaps alone, but rather are only reproduced in the calculations if account is taken of the strong variation of the electronic transition moment with internuclear distance caused by the rapid change from Rydberg to valence character in the region of the 32; curve crossin g. Ili~er~ying less intense and previously unidentified bands are similarly indicated to result from transitions to a mizxed Rydberg-valence 3~u species.