The present paper reports on experimentally obtained results of fast propagating deflagrations, the transition-process from deflagration to detonation, and detonations in hydrogen-air mixtures. These combustion phenomena are investigated by means of various sophisticated optical and conventional measurement-techniques like the Laser-induced Predissociation Fluorescence, which, in particular, gives a new insight into the understanding of these supersonic combustion-modes. Focus is put on the regime of the lean detonation-limit, depending on both, the mixture-composition and the dimension of the test-facility. For this limit criteria of empirical character have been applied for hydrogen-safety considerations until now. This study reports that a transition into a detonation of a fast-propagating flame is possible for leaner mixture-compositions as they are covered in the empirical criterion down to the theoretical detonation limit of the test-facility. It was observed that a detonation is not the most dangerous combustion mode. For mixture-compositions between the theoretical and the empirical detonation limit, it is as well possible that the flame propagates as a supersonic deflagration with the same velocity as the leading shock-wave. The peak-pressure of this combustion mode can be more than two-times higher compared to that of a detonation.