We present a perturbative analysis of a Rabi model where the coupling between the quantized single-mode electromagnetic¯eld and the two-level atom depends on the¯eld intensity. Upon modeling the matter-radiation coupling through the Holstein-Primako® realization of algebra suð1; 1Þ, we evaluate¯rst-and second-order eigenenergies and eigenstates both in the weakcoupling regime (atom transition frequency smaller than the coupling strength) and in the strong-coupling regime. In the¯rst case, among various e®ects, we observe a quadratic dependence on the photon number of energy eigenvalues and the possible formation of level doublets. In the strong-coupling case, the perturbative analysis becomes considerably complex due to the suð1; 1Þ-valued form of the unperturbed Hamiltonian. The critical condition for the transition to an almost continuous spectrum is found in terms of the model parameters.