The detonation processes in chemically active bubble liquids under elevated initial pressures are investigated theoretically. It is shown, that supersonic regimes of wave propagation can exist, if the initial pressure is relatively high and the volume fraction of the bubbles is relatively small. Characteristic values of the bubble detonation wave pressure at sub- and supersonic regimes differ by an order of magnitude. The principal possibility of detonation wave structure transformation in the case of propagation in the mixture with high initial pressure and longitudinal gradient of bubble volume fraction is predicted. The leading shock may transform into a smooth wave of compression. The Chapman-Jouguet conditions for self-sustaining supersonic bubble detonation wave is obtained. A model of shock induced single bubble dynamics and ignition taking into account the real properties of the liquid, inter-phase transition processes, mechanical mixing of phases, ignition delay and continuous shift of chemical equilibrium have been described. Calculations for the oxygen containing bubble in liquid cyclohexane have been performed. (C) 2003 Elsevier Science Ltd. All rights reserved.