A class of resonant absorbing cross sections was found for which there are simple exact solutions of the neutron moderation equation. Some of these solutions are compared with corresponding numerical solutions obtained by the methods of Rowlands, Nordheim, and Finkelstein. The first two methods are accurate for narrow and intermediate absorption resonances but develop instability when relatively strong (with respect to scattering) absorption extends for a few or more collision intervals. Then only the third method may be used with confidence.