Abstract The proton spin-lattice relaxation time T1 in the nemaic and smectic A phases of the liquid crystal N-p-cyanobenzylidene-p-n-octyloxyaniline was measured at several Larmor frequencies in the range of 5 to MHz. By extrapolating to infinite Larmor frequency, the relaxation rates due presumably to molecular diffusion were obtained at various temperatures. An activation energy for molecular diffusion in the mesophases was determined to be 3.4 Kcal/mole from these extrapolated values. At a low Larmor frequency (e.g. 5.5 MHz), the observed relaxation rate just above the smectic A-nematic (SN) transition canbe attributed t the following relaxation mechanisms: molecular diffusion, long range nematic director fluctuations and short range smectic order flectuations. The calcuated relaxation rate due to the short range smectic order fluctuation in the nematic phase was found to depend critically on temperature with a critical temperaute close to the SN tranistion Temperature.