We report a new method for continuous hydrogenation in supercritical fluids (CO2 or propane) using heterogeneous noble metal catalysts on Deloxan aminopolysiloxane supports. The method has considerable promise both for laboratory-scale hydrogenation and for the industrial production of fine chemicals. It can be applied to a wide range of organic compounds including alkenes, alkynes, aliphatic and aromatic ketones and aldehydes, epoxides, phenols, oximes, nitrobenzenes, Schiff bases, and nitriles, Conversion of starting materials, product selectivity, and space-time yields of the catalyst are all high, and the reactors themselves are very small (5- and 10-mL volume). Supercritical hydrogenation enables the reaction parameters to be controlled very precisely. Results are presented for a series of different reactions showing product distributions, which are dependent on temperature, pressure, H-2 concentration, and the loading and nature of the catalyst. The hydrogenation of cyclohexene has been studied in some detail, and our results are related to the phase diagrams of the ternary system cyclohexane + CO2 + H-2, which we present in a novel way, more suited to continuous reactors. Finally, we report that the supercritical hydrogenation of isophorone has advantages over conventional methods.