The measurement of the minimum critical energy that should be released inside a volume to be demolished to initiate the detonation is presented. A criterion based on the concept of the incubation time for the process of direct detonation initiation is proposed. The incubation time of the detonation process is directly connected with the process preceding the attainment of the steady regime for the detonation-wave propagation, including the chemical process. The criterion introduced to estimate the detonation conditions in the experiments is introduced. The detonation in the stoichiometric hydrogen-oxygen mixture was initiated by electric discharges of different frequencies and amplitudes up to detonation wave had been formed. The experimental conditions of the results are well consistent with the values of the critical energy obtained. The calculation results exploiting the new detonation criterion are compared with the experimental data.