Robust, routine, and rapid instrumental methods for the determination of the authenticity of edible oils, and the detection of adulteration, are continually being sought. In this paper, we compare mid-infrared and Raman spectroscopies for their ability to discriminate between oils of differing botanical origin and for their ability to detect added adulterants. Furthermore, we used sufficient numbers of samples to permit a comparison of some of the chemometric methods (linear discriminant analysis, artificial neural networks) available and looked at the results obtained when the two spectroscopic datasets were combined. We show that mid-infrared spectroscopy, in combination with linear discriminant analysis, gave the best classification rates and adulteration detection levels compared to Raman or combined data.