The dynamic behavior of a nematic liquid crystal is investigated by photon correlation spectroscopy. Two relaxation modes, the so-called splay and twist, are identified for a specific experimental geometry involving the directions of the wave vector q, the polarizations of the incident and scattered beams, and the vector director of the nematic liquid crystal n, The results obtained in this work are in good agreement with theoretical predictions describing the dynamics in nematic Liquid crystals. The relaxation rates are in reasonable agreement with those reported for the splay mode in earlier experimental results using the same optical configuration, as well as with those for the twist mode using a more difficult experimental geometry. We emphasize here that the relaxation times of both modes may be obtained simultaneously using a relatively simple experimental geometry.