Chemically-reduced graphene-oxide-supported gold nanoparticles and traces of iridium are considered here together with loadings of platinum as catalytic materials for reduction of oxygen in alkaline and acid media, respectively. Comparison is made to the analogous systems based on conventional Vulcan carbon carriers. Gold nanoparticles are prepared by the chemical reduction method, in which the NaBH₄-prereduced Keggin-type phosphomolybdate heteropolyblue acts as the reducing agent for the precursor (HAuCl₄). Polyoxmetallate (PMo₁₂O₄₀^3-) capping ligands stabilize gold nanoparticle deposits, facilitate their dispersion and attachment to carbon supports. Indeed, it is apparent from the independent diagnostic voltammetric experiments (in 0.5 mol dm^-3 H₂SO₄) that heteropolymolybdates form readily stable adsorbates on nanostructures of both gold and carbon (reduced graphene oxide and Vulcan). It is reasonable to expect that the polyoxometallate-assisted nucleation of gold has occurred in the proximity of oxygenated defects existing on carbon substrates. Under conditions of electrochemical diagnostic experiments (performed in 0.1 mol dm^-3 KOH) the phosphomolybdate adsorbates are removed from the interface as they undergo dissolution in alkaline medium; and the Au nanoparticles (Au loading, 30 µg cm^-2) remain well-dispersed on the carbon as evident from transmission electron microscopy. High electrocatalytic activity of the reduced-graphene oxide-supported Au nanoparticles toward reduction of oxygen in alkaline medium is demonstrated using cyclic and rotating ring-disk electrode (RDE) voltammetric experiments. Among important issues are possible activating interactions between gold and the support, as well as presence of structural defects existing on poorly organized graphitic structure of reduced graphene oxide (as evident from Raman spectroscopy). When using the silica or titania functionalized reduced graphene oxide as carriers for Au (or Ir) and Pt nanoparticles, the resulting systems have exhibited typically higher (certainly not lower) O₂-reduction currents (relative to those recorded at conventional Vulcan-supported Pt at the same loading) in acid medium (0.5 M H₂SO₄). The RDE data are consistent with even lower formation of hydrogen peroxide. Furthermore, the durability of this family of catalysts was outstanding. Finally, by doping the reduced graphene oxide supported Pt with traces of Ir (<1 µg cm^-2), decreases amounts of produced H₂O₂ (<1%) at potentials 0.6 V (vs RHE) or lower.