In analyzing atomic systems undergoing interactions with external fields that are nearly resonant with two, and only two of the atom's energy levels, one commonly employs a two-level or resonance approximation in which all states of the atom are neglected except for the two in resonance with the field. In this paper, we examine the assumptions necessary to make the transition from a differential equation for the exact polarization of an atomic system to the corresponding equation in the two-level approximation. Only when one includes contributions from states outside the two-level subspace does he find the exact equation reduces to the two-level equation within correctional factors of an intuitive nature.