Several experiments are described that relate to the application of new regimes of radiation action on enzymes in vitro and some other materials. These regimes have recently come into practice due to the appearance of a new generation of devices with very short high-energy pulses of ionizing radiation. It is shown that the term "flash radiation biochemistry" in its perfect sense has to be used at the condition of the overlapping individual effective interaction microvolumes (e.g. spurs and blobs) realized during a time interval (radiation pulse duration) that is low compared with the corresponding physical-chemical process. In this situation a number of unexpected effects occur at very low absolute doses. These processes are analyzed in terms of their non-stationary and non-diffusive developments.