New dynamic aspects of the catalysis of methanol oxidation reaction (MOR) have been studied using quantum mechanical calculations applied to the support–catalyst cluster interactions and surface diffusivity of adsorbed intermediates. For very small catalyst–support clusters, we have found a strong enhancement of the ligand effect for bimetallic catalysts of the type Pt_nM_m attributed to the decreased local density of states near the Fermi level of Pt atoms neighboring the additive metal atom M. This enhancement results in a decreased barrier for surface diffusion of adsorbed CO_ad through the cooperative diffusion mechanism, based on structural relaxation of the catalyst–support cluster, proposed in this work. The strong ligand effect dominates over the Schwoebel potential and trapping well effects, being responsible for accumulation of poisoning intermediates at step sites on the catalyst surface and gradual decrease of catalytic activity with decreasing size of catalyst nanoparticles. The lattice relaxation and strong ligand effects in small catalyst–support clusters lead to lower adsorption energy for CO_ad and thus, to higher reactivity and mobility of reactants and intermediates. The experimental investigations included submonolayer films of bi-functional catalysts (PtRu, PtFe) deposited on novel nanostructured supporting materials, designed with the goal of achieving high variability of their electronic and chemical properties to influence the catalytic activity of sub-monolayer catalyst. The mesoscopic TiO₂ supporting film formation was investigated using EQCN, pulse voltammetric and AFM techniques. The conditions for the formation of monodispersed TiO₂ nanoparticles with regular nanopores (nanotubes), 20–80 nm in diameter, were described. It follows from EQCN and voltammetric measurements and AFM image analysis that the nanopores are formed by a dissolution-precipitation mechanism. The catalysts, Pt and PtRu, deposited on supporting nanoporous TiO_2−x films, were used to study MOR. A lower poisoning effect for cluster PtRu on a TiO_2−x support film than that for unsupported PtRu or bare Pt catalysts has been observed. These effects have been attributed to differences in CO_ad binding energy and lowering of activation energy for surface mobility leading to a more facile 2D diffusion of CO_ad from Pt sites to Ru and the supporting TiO_2−x. The substrate–catalyst interactions were further investigated using quantum mechanical calculations performed for a model TiO₂ nano-ring (representing an orifice of a TiO_2−x nanotube studied experimentally) with adlayers of Pt, Ru and Fe catalysts. We have found unusually strong electron delocalization effects for Pt₂Fe₂ clusters on (TiO₂)₄ as compared to (TiO_2−x)₄Pt₂Ru₂. We have also analyzed various states in surface diffusion of CO_ad on bimetal clusters supported on (TiO₂)_n and observed considerable dynamic widening of metal-to-metal atom distances induced by CO adsorption (up to 9% for Pt–Pt distance and up to 15% for Fe–Fe distance). We propose that this new dynamic effect leading to cooperative surface diffusion may be further explored in designing novel nanoparticle catalysts.