The spectrum of the multigroup-multipoint operator with delayed neutrons is studied under the assumption of a common fission spectrum. Using the fact that the fission operator is proportional to a projector, the Weinstein-Aronszajn technique for degenerate perturbation can be used. The general problem is first reduced to a problem without delayed neutrons. The high degeneracy of the spectrum is further examined and connected with the definition of “clusters.”