A general formalism has already been derived for the inversion of the Boltzmann high-energy operator in particle-beam-sustained molecular plasma discharge. This inversion is possible provided the separation between 'bulk' (elastic processes dominant) and 'tail' (inelastic processes dominant) of the electron distribution function occurs very suddenly. Most molecular plasmas satisfy this model. However, referring to the scaling laws derived from this formalism, molecular oxygen appears as an important exception. Owing to low threshold metastable state excitations, the 'bulk' and the 'tail' of the electron distribution function are separated by an intermediate region where elastic and inelastic collisions are equally important. This problem is solved analytically. Using experimental parameters of gun jet electrons studied at Orsay by Pointu and Zeller, we obtain significant departures from Maxwellian behaviour for energies greater than the first metastable threshold (0.98 eV). The intermediate region between the first metastable threshold and the first electronic threshold (4.5 eV) is characterized by a 'plateau' in the electron energy distribution. These results are absolutely necessary if this intermediate region is to be matched to the 'bulk' of the electron distribution function in order to obtain the electron density and temperature which will be calculated and compared to those of A M Pointu and P Zeller in a forthcoming paper.