The dynamics of an initially critical bubble after a small (as small as is wished) perturbation of its radius has been examined. Dependences of the radius, the vapor pressure and the rate of change of the bubble radius on the time from the perturbation instant have been obtained. As a result, a new formula for the specific nucleation rate in stretched and superheated liquids has been deduced with the help of the well-known theory of fluctuation nucleation. To check the formula suggested, experiments were conducted on the superheating of Freon 11 and dodecane in the pressure range from -10 MPa to +1 MPa. A satisfactory agreement between calculation and experiment has been obtained, which gives grounds to suggest using the comparatively simple formula obtained in the practice of calculating the dynamics of explosive boiling-up. (C) 2019 Elsevier Ltd. All rights reserved.