Neutron scattering measurements of partially deuterated polystyrene (PS) samples-PSd3 with deuterated main Chain and PSd5 with deuterated phenyl rings - have been carried out below the glass transition temperature (T-g = 373 K) of the polymers by means of time-of-flight (TOF) and backscattering techniques (BS). Analysis of the data was performed putting emphasis on slow relaxation motions at t > 2 ps. Results show that hydrogens in phenyl rings have higher mobility than those in the main chain. The mean square displacement, < u(2)>, of the main chain on the other hand, is almost indistinguishable from those reported for chemically simpler polymers. The intermediate scattering functions obtained by Fourier transformation of experimental data in the TOP Window indicate than < u(2)> is mainly due to motions faster that similar to 2 ps, and that secondary relaxations have little effect on its value. In contrast to previous observations in several polymers containing phenyl rings in the main chain, rings in PS do not exhibit generalized 180 degrees flips, and the quasielastic scattering of phenyl rings in PS at t > 2 ps (including the BS window) can be reasonably well described by oscillations of increasing amplitude with temperature and mean activation energy of 021 eV. Our results support those NMR works which claim a low fraction of flipping rings for PS below T-g, and low amplitude motions for the origin of delta- and gamma-relaxations.