The degenerate many-body perturbation theory in Brandow's diagrammatic expansion is applied to 16 excited states of H2 at two internuclear separations. A single set of molecular orbitals at each separation is used for all states. Energy corrections up to third order (inclusive) are calculated, and higher-order effects are estimated by geometric extrapolation. Results agree with best available values to 1-2 kcal/mole. Differences between Goldstone and Brandow diagrams are discussed.