The technical application of bimetallic core-shell particles, which are highly attractive because of their high electrocatalytic activity, depends crucially on their long-term stability under operating conditions. In the present multi-method study, we explored the stability of structurally well-defined Ru-core Pt-shell model systems during the CO oxidation (COOR) and methanol oxidation (MOR) reactions. These electrodes consist of a single-crystalline Ru(0001) substrate covered by epitaxial Pt films of one to three atomic layers. The reaction-induced modifications in the surface morphology were identified by scanning tunneling microscopy (STM) measurements performed before and after the electrocatalytic measurement, which reveal a higher stability for electrodes with around three layers of Pt (up to 1.4 V vs. the reversible hydrogen electrode) than for those with fewer layers. Differential electrochemical mass spectrometry (DEMS) measurements carried out during the COOR allow separation of the COOR currents from surface redox processes, providing insight into the role of surface oxidation / reduction processes during the COOR. Operando surface X-ray diffraction (SXRD) measurements performed during electro-oxidation of methanol confirm the much higher stability of the electrodes with three Pt layers. The main conclusion of this work is that during the electro-oxidation of organic molecules, the stability of the electrodes is, in general, improved due to the reactive removal of OH/O species from the surface.