The effect of volume concentration and particle diameter on the velocity of the detonation wave (DW) in hydrogen/oxygen and a methane/oxygen mixtures with addition of inert particle cloud was investigated based on the developed physical and mathematical model of weakening and suppressing the detonation process in the mixtures, which takes into account the detailed kinetics of chemical reactions. The concentration limits (by volume concentration of particles) of detonation in mixtures of hydrogen/oxygen, methane/oxygen, and methane/hydrogen/oxygen were obtained. The comparison of the detonation suppression data in these mixtures revealed that the critical volume concentration quenching DW highest in the methane/hydrogen/oxygen mixture and the lowest in the hydrogen/oxygen mixture. Geometric limits of detonation are determined, and a comparison with similar results predicted by the simple "frozen" model is performed.