A class of bound-state problems which represent the interaction between a system of N two-level atoms and an electromagnetic radiation via an m-photon process is studied, with m = 1; 2; 3;.... We also evaluate some nonlinear effects usually related with the polarisability of the medium and with the dependence on the intensity of the radiation field on the matter-radiation interaction. We obtain exact values for the eigenstates and eigenvalues for all values of total angular momentum of the system and all possible number m of photons involved in the interaction. We give explicit analytic expressions for small numbers of atoms and discuss some aspects of the composition of the eigenstates and of the spectra obtained in these cases.
