Essential oils are amongst the most complex samples an analyst can face in terms of the number of compounds involved. In many cases, minor components are of interest as they can impart a distinctive fragrance character to the oil. Because of the closely related structures and molecular weights among terpenes, positive identification of individual compounds is very difficult with a single chromatographic technique. Further, most of the analytical information is lost when a single technique is used because of the limited peak capacity and the resulting peak overlap. For many years, gas chromatography coupled to mass spectrometry (GC-MS) has been the benchmark technique for qualitative and quantitative analysis of essential oils. Retention indices and mass spectra have to be used in combination for confirmation of the identity of components in an essential oil. Other multidimensional or hyphenated techniques also offer advantages that aid in the identification of essential oil components. This thesis demonstrates the application of a comprehensively coupled supercritical fluid and fast temperature programmed gas chromatograph (SFCxGC) to the analysis of essential oils. An SFCxGC instrument was used to analyse the essential oils of Cymbopogon (lemongrass), Artemisia afra (wilde als), Tagetes minuta (kakiebos) and Pelargonium (geranium) species. The unique application of a porous layer open-tubular (PLOT) column, used in conjunction with supercritical carbon dioxide is demonstrated to effect group separation of polar, oxygenated compounds. This separation and elution of very polar compounds from a silica gel column is believed to occur due to the reduced phase ratio (??) of the system obtained by increasing the volume available to the mobile phase compared to that of a packed column. This separation obtained in the SFC is used to separate essential oils into different chemical classes such as non-polars, ethers, alcohols. Separated chemical classes are re-injected on-line by use of a modulator into a fast, second dimension, temperature programmed GC to effect separation of individual compounds based on their volatility. The entire sample is analysed by both the SFC and GC in such a way that the resolution obtained in the first dimension is conserved by the GC analyses. By using a range of standards, some of the peaks in these oils could be assigned. The identification of compounds was greatly aided by the combination of the two separation dimensions. The comprehensive two-dimensional technique arranges component peaks in a plane from which chemical class and volatility information of each component is readily obtained. The elution pattern within the two-dimensional chromatograms may also be used for direct comparison of oils without identification of the components in the essential oils.