The present short review article reports four examples of catalytic reactions realised on relatively well-defined supported catalysts. These catalysts were conceptually designed and prepared by a Surface Organometallic Chemistry (SOMC) approach. They were designed for achieving the olefin metathesis reaction, the Ziegler-Natta depolymerisation, the low temperature hydrogenolysis of alkanes and the alkane metathesis reaction. These reactions are "related" to the metathesis of inert bonds. The first example is the silica-supported rhenium (VII) carbene species [(dropSi-O)-Re(dropC-t-Bu)(=CH-t-Bu)(CH2-t-Bu)] obtained by grafting Re(dropC-t-Bu)(=CH-t-Bu)(CH2-t-BU)(2) on silica. This catalyst has turned out to be very active in the propene metathesis reaction (initial T.O.F. = 0.25 mol/mol Re/s) after an initiation step involving a cross-metathesis reaction between the neopentylidene ligand and propene. The silica or silica-alumina-supported zirconium hydride(s) catalyse(s) the "depolymerisation" of polyethylene into lower oligomers and "diesel range hydrocarbons". The depolymerisation reaction mechanism involves a p-alkyl transfer which is the microscopic reverse of the "Cossee" mechanism of olefin insertion into a metal alkyl bond. Moreover, in the case of low-density branched polyethylenes (LDBP), the cleavage of the polymer chain occurs preferentially on the branches of the initial polymer. Therefore, the branched initial polyethylene is transformed into a linear one. Besides, recent advances in NMR spectroscopic techniques have highlighted that the zirconium hydride catalyst contains in fact two surface species: a zirconium monohydride (major) and a zirconium dihychide (minor). The silica-supported tantalum hydride, [(dropSiO)(2)Ta-H], and the silica-supported zirconium hydrides [(dropSiO)(2)ZrH2] and [(dropSiO)(3)Zr-H] both catalyse the low temperature hydrogenolysis of alkanes but with a major difference between the two metals-tantalum hydride is able to cleave the C-C bond of ethane whereas zirconium hydrides are not. In fact, the C-C bond cleavage reactions go through different pathways: in the case of Zr the pathway of C-C bond cleavage obeys a p-alkyl transfer mechanism while, in the case of Ta, another pathway is required, which involves either sigma-bond metathesis, oxidative addition or carbene mechanism. Notably, the tantalum hydride, catalyst has also been found to be active in the alkane metathesis reaction. During this reaction, two different processes occur simultaneously: the productive alkane metathesis which leads to higher and lower alkane homologues and the scrambling of the initial alkane reagent. (C) 2003 Elsevier B.V. All rights reserved.