NOVELTY - Production of catalysts containing mono- or multi-metal oxide (I) particles, fixed to a support (II), comprises hydrolysis and (co)condensation of salt(s) of sub-group IIIb, IVb, Vb, VIb, VIIb, VIII, Ib or IIb metal(s) (M') in basic aqueous solution; and in situ immobilization of the water-soluble (I) colloid, stabilized with hydroxide ions, on (II), which is also suspended in the solution.    USE - The catalysts are used as catalysts or catalyst precursors for hydrogenation, oxidation or linking reactions (all claimed), including carbon-carbon linking reaction. The catalysts, preferably containing platinum/ruthenium/molybdenum (Pt/Ru/Mo), Pt/Ru/osmium (Os), Pt/Ru/tin (Sn) or Pt/Ru/Os/iridium (Ir) multimetal oxides, are also used as electrocatalysts in fuel cells (all claimed).    ADVANTAGE - The in-situ immobilization process is very simple and requires only one stage, without further treatment or activation. It also uses water as solvent, which is cost-effective and environmentally friendly; and ensures almost complete conversion of the metal precursor to oxide(s) (no metal loss). Up to 20 wt.% metal can be immobilized in a single stage and more by repeated treatment. The process gives almost monodisperse nanoparticles, i.e. high dispersion of the metal(s). The oxide particles have high structural stability at high temperature and are dispersed uniformly on the support, rather than concentrated on the surface. The catalyst powder can be purified and isolated easily by dialysis, freeze drying or centrifuging. The stoichiometry of bimetals can be regulated over a wide range; and the oxide catalyst powder can be reduced without significant change in stoichiometry and particle size distribution. Unlike supported metal catalysts, the (multi)metal oxide catalysts can be handled in air.    DETAILED DESCRIPTION - Production of catalysts containing mono- or multi-metal oxide (I) particles with diameters of 0.5-5 nm, fixed to a support (II), comprises hydrolysis and (co)condensation of salt(s) of sub-group IIIb, IVb, Vb, VIb, VIIb, VIII, Ib or IIb metal(s) (M') in basic aqueous solution; and in situ immobilization of the water-soluble (I) colloid, stabilized with hydroxide ions, on (II), which is also suspended in the solution.    INDEPENDENT CLAIMS are also included for:    (1) Supported catalysts with metal oxide particles produced by this process;    (2) Supported catalysts with metal oxide particles with diameters of 0.5-5 nm, fixed to a support, in which the particles contain oxides of not less than 3 metals, one of which can be a main group metal and the others metals, of 2 metals M', one platinum (Pt) and the other tin (Sn) or iridium (Ir), ruthenium (Ru), iron (Fe) or tungsten (W) or another M' or one Ir and the other M'.