We have investigated multiple ionization of N(2) and O(2) molecules by 52 nm extreme-ultraviolet light pulses at the free-electron laser facility SCSS in Japan. Coulomb break-up of parent ions with charge states up to 5+ is found by the ion-ion coincidence technique. The charge-state dependence of kinetic energy release distributions suggests that the electrons are emitted sequentially in competition with the elongation of the bond length.