We present results of extensive computer simulations and theoretical analysis of vibrational phase relaxation of a nitrogen molecule along the critical isochore and also along the gas-liquid coexistence. The simulation includes all the different contributions [atom-atom (AA), vibration- rotation (VR), and resonant transfer] and their cross-correlations. Following Everitt and Skinner, we have included the vibrational coordinate (q) dependence of the interatomic potential. It is found that the latter makes an important contribution. The simulated results are in good agreement with the experiments. Dephasing time (tau(v)) and the root mean square frequency fluctuation (Delta) in the supercritical region are calculated. The principal important results are: (a) a crossover from a Lorentzian-type to a Gaussian lineshape is observed as the critical point is approached along the isochore (from above), (b) the root mean square frequency fluctuation shows nonmonotonic dependence on the temperature along critical isochore, (c) along the coexistence line and the critical isochore the temperature dependent linewidth shows a divergence-like lambda-shape behavior, and (d) the value of the critical exponents along the coexistence and along the isochore are obtained by fitting. It is found that the linewidths (directly proportional to the rate of vibrational phase relaxation) calculated from the time integral of the normal coordinate time correlation function [C-Q(t)] are in good agreement with the known experimental results. The origin of the anomalous temperature dependence of linewidth can be traced to simultaneous occurrence of several factors, (i) the enhancement of negative cross-correlations between AA and VR contributions and (ii) the large density fluctuations as the critical point (CP) is approached. The former makes the decay faster so that local density fluctuations are probed on a femtosecond time scale. The reason for the negative cross-correlation between AA and VR is explored in detail. A mode coupling theory (MCT) analysis shows the slow decay of the enhanced density fluctuations near critical point. The MCT analysis demonstrates that the large enhancement of VR coupling near CP arises from the non-Gaussian behavior of density fluctuation and this enters through a nonzero value of the triplet direct correlation function. (C) 2003 American Institute of Physics.