An equation set describtng single particle excitations for excitation energies which are small compared with the chemical potential of the system can be obtained by investigating the analytical properties of the Green's functions and taking into account pair correlation. The equations are valid for an arbitrary interaction law. Equations are derived which describe the excited states of a system with a finite number of particles with an accuracy to terms of the order of N/sup -//sup 1//sup ///sup 3/ It is indicated how the results can be applied to real nuclei. (auth)