Intermediate states formed during the dissociative recombination of molecular ions with electrons can play sionificant roles in determining the magnitude of the total rate coefficient. These resonances are Rydberg states of two types, that is, they can have the ground or excited states of the ion as a core. Those with the excited cores have a fundamentally different excitation mechanism than those with the ground state core. The importance of excited core states in dissociative recombination has received only limited attention in the literature. Theoretical calculations on the dissociative recombination of N-2(+) are reported which compare the two types of resonances. Potential curves, electronic widths, cross sections, and rate coefficients are calculated for dissociative recombination along the 2(1)Sigma(+)(g) state, one of several routes for the dissociative recombination g of N,. The ground core resonances, in this example, are relatively unimportant compared to those with the excited core. Inclusion of the excited core resonances increases the rate coefficient by about a factor of 4 at room temperature, but the increase is not enough to establish 2(1)Sigma(+)(g) as the dominant dissociative route