Experimental studies have demonstrated that the vibrational dephasing of overtones do not always follow the quadratic quantum number (n) dependence predicted by the Kubo-Oxtoby theory of vibrational line shapes. While the reason for this failure of the theory is not quite clear yet, a recent theory suggested that the pronounced Gaussian time dependence of the frequency-modulation time-correlation function (tcf) could be a possible reason [Gayathri cr al., J. Chem. Phys., 107, 10381 (1997)]. The theoretical study was based on a mode coupling theory calculation of the force-force time-correlation function that is required in the calculation of the frequency-modulation tcf. In order to test this and other predictions of the above study, detailed computer simulations of two neat liquids have been carried out. The systems studied are N-N stretch in liquid N-2 and the C-I stretch in CH3I. It is found that although the frequency-modulation time-correlation function is largely Gaussian in both the cases, the overtone dephasing remains largely quadratic in n for N-2. For methyl iodide, on the other hand, a pronounced sub-quadratic n dependence has been observed. Both the theory and the computer simulations suggest that this nonquadratic dependence can be expected when not only the decay of the frequency time-correlation function is Gaussian but the time scale of decay of the frequency-modulation tcf is comparable to that of the normal coordinate. The latter can happen when the following conditions are satisfied. First, the frequency of the normal mode should not be too large. Second, the mean-square fluctuation of the frequency-modulation and the anharmonicity coefficient of vibration should be large. It is found that both for N2 and CH,I, the resonant energy transfer between different molecules is significant. The effect of rotational-vibrational coupling, on the other hand, is found to be negligible for the systems studied.