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 wave (DW) velocity deficit versus 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: (1) stationary propagation of weak DW in the gas suspension, (2) galloping propagation of detonation, (3) destruction of the detonation process and transformation to wave of turbulent burning. It was determined that the mechanisms of detonation suppression by micro- and nanoparticles are closed and lie in the splitting of a DW to frozen shock wave and ignition and combustion wave. Concentration limits of detonation were calculated. It turned out that concentration limits (on particle volume concentration) of detonation are quite similar for particles with diameters ranging from 10 nm to 1 mu m.