The physical and mathematical models for the description of the detonation process in mixtures of hydrogen-oxygen, methane-oxygen and silane-air in the presence of inert nanoparticles were proposed. On the basis of these models the dependencies of detonation velocity deficit vs the size and concentration of inert nanoparticles were found. Three regimes of detonation flows in gas suspensions of reactive gases and inert nanoparticles were revealed: - stationary propagation of weak detonation wave in the gas suspension, - galloping propagation of detonation; - destruction of the detonation process. It was determined that the mechanisms of detonation suppression by micro- and nanoparticles are closed and lies in the splitting of a detonation wave to frozen shock wave and ignition and combustion wave. Concentration limits of detonation were calculated. It turned out that in the transition from microparticles to nanoparticles the detonation suppression efficiency does not increase.