Statistical mechanical chemical equilibrium calculations of N-2 and O-2 show that these molecules dissociate behind strong shock waves. Our determination of accurate intermolecular potentials has required the consideration of the dissociation products N and O. Our previous theoretical efforts to predict the thermodynamic properties of these molecules relied in part on corresponding states theory and shock wave data of argon, without consideration of the dissociation products. Recent high-pressure Hugoniot measurements, however, allowed a more accurate determination of the potentials and the explicit inclusion of the dissociation products. The best fit to the data is obtained with the exponential-6 coefficients, for O-2-O-2 : epsilon/k=125 K, r*=3.86 Angstrom, alpha=13.2; for O-O : epsilon/k=700 K, r*=2.40 Angstrom, alpha=11.0; for N-2-N-2 : epsilon/k=293 K, r*=3.91 Angstrom, alpha=11.5; and for N-N : epsilon/k=600 K, r*=2.47 Angstrom, alpha=10.0. The unlike pair interactions are obtained from these like interactions with a modified Lorentz-Berthelot rule. The coefficients in the modified Lorentz-Berthelot equations are k/l/m=1/1/0.93 for O-2-O- and k/l/m=1/1/0.90 for N-2-N interactions.