Today it is not known - neither qualitatively not quantitatively - how large the impact can be of the promoters on sensitivity to hydrogen-air detonation in hypothetical accidents at hydrogen-containing installations, transport or storage facilities. Report goal is to estimate theoretically an effect of hydrogen-peroxide (as representative promoter) on sensitivity to detonation of the stoichiometric hydrogen-oxygen gas mixtures. The classical H2-O2-Ar (2:1:7) gas mixture was chosen as reference system with the well established and unambiguously interpreted experimental data. In kineticsimulations it was found that the ignition delay time is sensitive to H2O2 addition for small initial H2O2concentrations and is nearly constant for the large ones. Parametric reactive CFD studies of two-dimensional cellular structure of 2H2-O2-7Ar-H2O2 detonations with variable hydrogen peroxide concentration (up to 10 vol.%2 were also performed. Two un-expected results were obtained. First result: detonation cell size is practically independent upon variation of initial hydrogen peroxideconcentration. For practical applications it means, that presence of hydrogen-peroxide did not change drastically sensitivity of the stoichiometric hydrogen-oxygen gas mixtures. These theoreticalspeculations require an experimental verification. Second result: for large enough initial H2O2concentrations (> 1 vol.%2at least), a new element of cellular structure of steady detonation wave was revealed. It is a system of multiple secondary longitudinal shock waves (SLSW), which propagates inthe direction opposite to that of the leading shock wave. Detailed mechanism of SLSW formation is proposed.