This thesis covers the investigation of new catalytic systems for the aerobic oxidation of chemicals derived from bio-renewable sources. The effects of different factors and conditions on the reactions were examined. The employed catalysts were characterized by physisorption measurements, SEM, TEM, EDS, XRF and other methods. Supported gold and ruthenium hydroxide catalyst systems were explored for the aerobic oxidation of 5-hydroxymethylfurfural (HMF) to 2,5-furandicarboxylic acid (FDA), a potential polymer building block for the plastic industry, or its dimethyl ester (FDMC). High product selectivities and yields were obtained under optimized conditions. Heterogeneous catalysts consisting of Au nanoparticles on different supports were shown to efficiently oxidize HMF to FDA or FDMC in water or methanol, respectively. Additionally, the reaction conditions were shown to be adjustable for the exclusive production of intermediate products of the oxidation. Catalysts consisting of Ru(OH)x deposited on metal oxide supports, such as, for instance, CeO2 and MgAl2O4, were employed in the aerobic oxidation of HMF in different ”green” reaction media, e.g. water and various ionic liquids, under base-free conditions. Moreover, a detailed study on the performance and stability of the ruthenium hydroxide catalysts on magnesium-containing supports under reaction conditions was conducted. The aerobic oxidation of HMF to form another value-added chemical, 2,5-diformylfuran (DFF), was also investigated with supported Ru(OH)x catalysts in organic solvents. The examined catalyst systems and reaction conditions were also shown to be applicable for the efficient oxidation of other substituted furans. Furthermore, novel catalytic systems comprising vanadia supported on zeolites were investigated for the aerobic oxidation of HMF to DFF in organic solvents, and a lixiviation study was performed. The oxidation of aliphatic alcohols over supported Ru(OH)x and RuOx catalysts is also described. The highly selective and efficient oxidation of ethanol to acetic acid was shown with supported Ru(OH)x and highly dispersed RuOx deposited on various metal oxides. Furthermore, this thesis presents the results of the catalytic aerobic oxidative degradation of higher alcohols over supported ruthenium hydroxide catalysts. A very efficient oxidative cleavage of vic-diols to form respective acids was also shown under examined conditions. Thus, the oxidative transformations of biomass-derived chemicals over different gold and ruthenium-based catalyst systems with oxygen as the abundant oxidant were explored.