The rhodium complexes [Rh(COD)(1)]BF4 (Rh(N−P)) and [Rh(COD)(2)]BF4 (Rh(N−N)), containing the new pyridylphosphine and bipyridyl ligands (1 and 2) with alkoxysilane groups, were tethered on the silica-supported palladium heterogeneous catalyst Pd−SiO2 to give the TCSM (tethered complex on supported metal) catalysts Rh(N−P)/Pd−SiO2 and Rh(N−N)/Pd−SiO2. Under the mild conditions of 70 °C and 4 atm of H2, the two TCSM catalysts are very active for the hydrogenation of arenes (PhCO2Me, PhOH, toluene, PhOCH3, PhCO2Et, 4-CH3C6H4CO2Et, dimethyl terephthalate) to cyclohexanes; the activities are higher than those of the separate homogeneous Rh(N−P) and Rh(N−N) complex catalysts, the silica-supported palladium catalyst Pd−SiO2, or the rhodium complex catalysts tethered on just SiO2. The catalysts are easily separated from the reaction mixtures and can be recycled several times without losing activity. Of the two TCSM catalysts, the higher activity for the hydrogenation of anisole to methyl cyclohexyl ether was observed for Rh(N−N)/Pd−SiO2, which gives a TOF value of 3060 mol of substrate converted/((mol of Rh) h) and a TO value of 14 500 mol of substrate converted/(mol of Rh) in 6 h. Reactions of acetophenone lead to hydrogenation of the arene ring, the carbonyl group, or both, depending on the catalyst (Rh(N−P)/Pd−SiO2 or Rh(N−N)/Pd−SiO2) and the solvent (heptane or ethanol).