Sr-90 and Cs-137 are two key fission products that are important in a number of radioactive waste or contamination clean-up scenarios. This thesis investigates the sorptiondesorption behaviour of these two radionuclides with a number of sorbents relevant to one of the legacy waste storage ponds on the Sellafield site. Sorption-desorption studies were undertaken on brucite (Mg(OH)2), UO2 and UO3 powders to represent components of the fine particulate sludge that has accumulated on the bottom of the pond, resulting from corrosion of the Magnox fuel elements. Brucite was found not to have a significant interaction with Sr-90 or Cs-137. However, organic molecules in the form of humic acid and Pseudanabaena catenata cyanobacterial growth supernatant were both found to enhance sorption interactions of Sr-90 with brucite. The effect of humic acid was pH dependent and appeared to control both sorption and desorption behaviour at pH 11.5. Uranium oxides had the most significant effect on controlling Sr-90 and Cs-137 sorption-desorption behaviour. In this work X-Ray Absorption Spectroscopy (XAS) showed that 90Sr sorbed strongly to both uranium oxides as a bidentate inner-sphere complex. Humic acid did not appear to alter the interaction of Sr-90 with UO2. For Cs-137 there was a significant, reversible interaction with both oxides, although the interaction was far stronger with UO3. Successful detection of stable Sr and Cs isotopes on uranium oxides was achieved with Laser Induced Breakdown Spectroscopy (LIBS).