Dynamical properties of acyl chains in the three polymorphic phases alpha, beta ', and beta of tristearin [C3H5(OCOC17H35)(3)] have been studied by means of incoherent quasielastic neutron scattering (IQNS) using selectively deuterated samples. The mean square displacement of hydrogen atoms, < U-2 >, was estimated from the scattering vector Q dependence of the elastic scattering component under the harmonic approximation. It was shown that the temperature dependence of < U-2 > was significantly different between the three phases. There was no marked difference in < U-2 > between these phases up to 193 K, and the < U-2 > value increased linearly with temperature. Although the beta phase remained linear up to 293 K, the alpha and beta ' phases started to show a nonlinear increase around 200 K, suggesting an anharmonic nature of molecular motions. The alpha phase exhibited the most conspicuous temperature dependence. These characteristics were ascribable to the difference in the lateral packing of acyl chains. Compared with the beta phase which has a tightly packed T// subcell, the beta ' and alpha phases have looser O perpendicular to and H subcells, respectively. The molecular motion in the alpha phase was analyzed using the model of uniaxial rotational diffusion in a onefold cosine potential. It has been clarified that the rotational fluctuation about the chain axis in the alpha phase is rather restricted compared with that in the rotator phase of n-alkanes.