A two-group study of neutron-wave propagation has been made in two crystal-line moderators—beryllium and graphite. For each moderator the results are reported at two temperatures: (i) room temperature and (ii) a rather low temperature. The effect of Bragg cut-off on the propagation of neutron-waves in these crystalline moderators is clearly brought out. It is found that for frequencies greater than a certain frequency fo, a pseudo-asymptotic mode exists even though cold neutrons fail to reach equilibrium. It is shown that in moderators at low temperatures, large phase difference between the two components of the wave (the cold neutrons and the rest) can develop for small source frequencies and this can lead to a considerable depression in the flux at some particular distance for some fairly well defined frequency.