Infrared bands and Raman lines recorded in the frequency domain have a counterpart in the time domain in the form of time-correlation functions, which are sensitive to molecular dynamics on the picosecond time scale. Time correlation functions and their variation with temperature have been calculated for the modes observed near 1601 and 1583 cm(-1) in the infrared spectrum of atactic polystyrene, The correlation functions can be modeled by assuming that there is a fast relaxation process characterized by a single relaxation time that is inhomogeneously broadened by a slower process, also characterized by a Single relaxation time. The fast modulation is of the order of 0.014 ps for both modes. Librational motions of the phenyl ring occur on the 0.01 ps time scale. suggesting that this mode of relaxation involves a rapid dephasing process. One cannot draw firm Conclusions. however, because dephasing and vibrational energy relaxation mechanisms cannot be separated by studies of simple band shapes alone. A slower process. with a relaxation time of the order of 1-10 ps, inhomogeneously broadens both modes. The slower process for the 1601 cm(-1) mode is relatively insensitive to temperature and mirrors the so-called "fast" transition seen in neutron diffraction studies of this polymer. The second fundamental mode. near 1583 cm(-1), is also inhomogeneously broadened, but the relaxation time calculated for this mode is far more sensitive to temperature as a result of anharmonic coupling to a combination mode that is probably mediated by lattice or bath modes. This provides a path for vibrational energy relaxation and sensitivity to dynamical transitions. A change in the modulation of the 1583 cm(-1) band becomes apparent about 10-20 degrees C below the thermally measured T, Relaxation times at first increase (from about 2 ps to near 10 ps) then decreases and become., negligible at temperatures near 180 degrees C. These results are consistent with theories of the glass transition. which predict a dynamical transition near 1.2T(g) and a crossover region between this temperature and the laboratory T-g.