The host NMR line‐width of CuMn alloys with 3 and 6 at% Mn is measured in an external field of 0.975 T. The temperature is varied from the paramagnetic regime down to the deeply frozen state far below the spin glass transition temperature Tf. The results are in good agreement with recent numerical mean field studies of Klauß et al. Whereas the field dependent part of the line‐width at higher temperatures scales with a Brillouin function Bs(H, T) it diminishes at lower temperatures. This is a result of the creation of transverse components of the spin expectation value 〈S〉 caused by impurity interactions which decrease the additional internal fields in spite of the increase of 〈S〉 with decreasing temperature. Supplementary measurements of the transverse relaxation time T2 show that dynamical effects which are not included in the mean field studies are of negligible influence in the time scale accessible to the experiment. At temperatures below T ≈ Tf/6 the line‐width shows an unexpected increase. Possibly this has to be attributed to a change in the NMR excitation function which is influenced by the transverse components of 〈S〉 and by an anisotropy field in combination with a NMR enhancement factor becoming significant in this temperature region.