An extension of the Fleming and Johnson procedure is presented for determining the molecular third-order susceptibility parameters from three characteristic intensities within a CARS line profile (I,,,, I,,+, &,id)+ For CARS excitation close to a molecular one-photon resonance, these three intensity values taken from one spectrum do not suffice for the determination of all relevant parameters. A simple procedure is given for overcoming this by combining the information from all the spectra within a concentration series, keeping the frequency of the CARS pump laser fixed. Uncertainty in the measured Imid value is overcome by applying a least-squares fit of the spectra.Results obtained from resonance CARS measurements for Rhodamine 6G in ethanol are given.