Abstract Total neutron cross sections have been measured for some hydrogenous compounds (acetylene, ammonia, methane) condensed at different low temperatures, and for neutron wavelengths between 1 Å and 12 Å. From the variation of the neutron cross section as a function of temperature and neutron wavelength some information is derived about the dynamical behaviour of the bound protons. An interpretation of the results is tried in terms of an effective Debye temperature characterizing each moderator. For solid ammonia the Debye-model fits rather well, but for methane it seems inadequate. There appears to be a good correlation between the values obtained for the inelastic scattering cross section, and the results of earlier measurements on the output of cold neutron sources.