Measurements of the proton spin-lattice relaxation rate (l/Tl) at a pressure of 1 bar in a single crystal of (TMTSF),PF6 (TMTSF is tetramethyltetraselenafulvalene) are reported for the magnetic field in the range 0.25-1.48 T aligned along the 6'and c*-axes over the temperature range 2-30 K. The methyl group rotation contribution to 1/T, is subtracted to obtain the spin density wave (SDW) contribution. Through measurements of l/T1 below and above the spin flop transition it is determined that

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... son fluctuations of the SDW are responsible for most of the relaxation. Depinning the SDW's by an electric field leaves l/Tl nearly unchanged, which indicates that the SDW and its fluctuation rate near 10' rad/s persist when the SDW is sliding. Analysis of the peak in l/T1 near 3 K on the applied magnetic field suggests that it represents a slowing of thermally activated fluctuations with an activation energy A/kB = 18.3 f 4.0 K, which is close to the single particle gap for this material. The contribution of critical fluctuations to l/T1 is consistent with the transition being weakly first order. Unlike the relaxation in the ordered phase, the contribution of the critical fluctuations is isotropic and has little, if any dependence on magnetic field.