Near and above the Néel point in FeF2, we observe an anomaly in the F19 NMR line width about six times stronger than the corresponding anomaly1 in MnF2. In a field H 0=14 kG applied along the c (antiferromagnetic) axis, the line width δνc increases by a factor of 20 upon cooling from T c+5°K to Tc+0.04°K. An empirical formula is δνc = Acε-nc, with nc = 0.69±0.05, Ac = 35 kHz, and ε = (T-T c)/Tc. With the applied field along the a direction we find δνa = Aaε-na, with n a = 0.50±0.05, and Aa = 45 kHz. These relations hold for 10-3<ε<10-1. At Tc+0. 1°K, δνc/δνa = 2.5±0.4. From the theory of Kubo and Tomita,2 the line width may be expressed 3 as δν(T) ∝ Σk[Szz(k, 0) + 1/2Sxx(k, ωL) + 1/2 Syy(k, ωL)], where S(k, ω) is the diffuse part of the scattering function, z is along H0, and ωL = γ19 H0=3.8×108 sec-1. Assume that the line width is due mostly to modes for which |k-k 0|≲ν1, where k0 is the antiferromagnetic mode and κ1 ∝ εν is the inverse correlation range. Then the temperature dependence of the relaxation rate Γc(k0) of the staggered mode can be deduced from our data. We find Γc(k0) ∝ κ1s where s = 2.1±0.25, when we assume ν=0.67. If we take ν=0.5 as was reported4 for MnF2, we find s=2.5±0.3. It is then possible that Scc(k0, 0) is significantly larger than Scc(k0, ωL) near Tc. In fact, this must be the case in order to explain the observed value of δνc/δν a within the framework of the Kubo-Tomita expression. Alternatively some additional source of broadening may be present. One possibility is the indirect nuclear-nuclear interaction5 as enhanced by the large spin susceptibilities in the critical region. A detailed account of our experiments will be published elsewhere. © 1969 The American Institute of Physics.