A family of molybdenum(VI) oxide hybrid solids with the general compositions [MoO3(tr)], [Mo2O6(tr)] and [Mo2O6(tr)(H2O)2] (tr = 1,2,4-triazole ligands bearing amine, pyrazole, 1H-tetrazole, and 1,2,4-triazole groups) have been shown to promote the epoxidation of cis-cyclooctene, the oxidative dehydrogenation of benzyl alcohol to give benzaldehyde, and the oxidation of benzaldehyde to give benzoic acid, using aqueous H2O2 as oxidant. All materials studied act as pre-catalysts and undergo chemical transformation in the presence of the oxidant to give the active oxidising species which, on the basis of characterisation data for recovered compounds, are either mononuclear or polynuclear oxo(peroxo)molybdenum(VI) complexes. Materials with one-dimensional (1D) structures led to homogeneous catalytic reactions with activities that were generally superior to those obtained with materials possessing more rigid 2D/3D structures containing bitriazole ligands. The latter were proposed to lead to interconverting mononuclear (poorly soluble) and dinuclear (soluble) species of the type [MoO(O2)2(L)] and [{MoO(O2)2(L)}2(μ-O)].