The dissolution process for gaseous oxygen in yba2cu3o6+2r and in la2cuo4+d, where r and d are the numbers of occupied sites, is 0.5 O2(g) = [dissolved o]. The statistical thermodynamic equation for the dissolution of oxygen in yba2cu3o6+2r is ago = rtln[[r/divided into p(o2] = -88,300 + 56.55 T - (75,200 - 218.3T)r - rt(1-r), where ago is the standard Gibbs energy change in j/mol[o], r = 8.3144 J/mol k, t is the temperature in k, and p(o2) is the oxygen pressure in atm. The corresponding equation for la2cuo4+d is ago - rtln[d/divided into p(o2) = -36,500 + 92t. Analyses of the published data suggest that for high-temperature superconductivity (1) a layered-type crystal structure appears to be essential, (2) excess oxygen plays a major role, and (3) at least one element capable of forming a peroxide, i.e., -o-o-chains, is also essential. The copper atoms play an important role in all the new oxide superconductors; however, other elements with their oxides having odd numbers of d-electrons might well lead to new higher tc super- conductors at high oxygen pressures.