the behavior of the chemical reaction of hydrogen-oxygen moleccules has an essential importance in the study of the combustion in rocket engines. A numerical method for the prediction of the behavior of the constant presseur adiabatic explosion of hydrogen-oxygen mixtures using Gear operator technique is presented. The analysis can solve for the chemical kinetics of the reaction ( temperature & composition), activation of the reaction, effect of the free radical generation rate on the thermal explosion behavior and for explosion limits (Ise 2nd, 3rd) at various presseures and initial temperatures of the einture. The case of stoichiometric ring ratio is computed and compared with published experamental data.