This thesis presents the first analysis of spatially resolved, far-UV reflectance spectra of Saturn’s icy satellites Rhea and Dione collected by the Cassini Ultraviolet Imaging Spectrograph (UVIS) during targeted flybys. The objective of this geochemical survey of Rhea’s and Dione’s leading and trailing hemispheres is to identify and explain the broad absorption feature centred near 184 nanometres. The secondary objective is to determine the presence of any minor impurities within the ice layers of these satellites by characterizing the location in wavelength space and shape of the 165-nm absorption edge due to pure water ice. To determine the precise position of the mid-point of the absorption edge, derivative spectroscopy is applied to the Cassini UVIS spectra. The presence of any non-water-ice molecules within the ice matrix and/or changes in the structure of the ice grains should cause a shift from the nominal position of the 165-nm absorption edge, or alter the slope of the absorption edge. The 165-nm absorption edge and 184-nm absorption feature have been observed in disk-integrated spectra of Rhea and other icy satellites in the Saturnian system. However, as of to date, there has been no satisfactory explanation for the 184 nm absorption feature. Cassini UVIS reflectance spectra are compared with modelled spectra derived using far-UV spectra of thin-ice specimens collected in laboratory experiments and Hapke theory. The results of the modelling show that the UVIS observations can be modelled by two molecules: simple chloromethanes beneath a layer of water ice or hydrazine monohydrate mixed in solid phase with water ice. A detailed analysis based on the astrochemistry and geomorphology of Rhea and Dione show that chloromethane molecules on their surfaces is difficult to explain, since their presence would require active subsurface oceans and an extensive network of fractures through their thick ice shells. On the other hand, hydrazine monohydrate is easier to explain since it can be produced via irradiation of ammonia ice by energetic particles originating from Saturn’s magnetosphere environment. It is also shown in the research that hydrazine can also be produced on Saturn’s largest moon Titan by irradiation of ammonia ice, or by chemical reactions involving water-ice and solid ammonia ice. Several possible alternative scenarios based on an analysis of both sinks and sources of chloromethane molecules and hydrazine are presented in this thesis