The rate of the quantum cavitation in normal fluid3Heand superfluid4Heat temperatures down to absolute zero has been studied. The effect of energy dissipation due to viscosity and the effect of the finite compressibility of a fluid are incorporated into the calculation of the quantum cavitation rate. Because of the dissipative processes, the kinetics of the quantum cavitation in3Heand4Heproves to be qualitatively different. In normal3Heit corresponds to the dissipative tunneling through a potential barrier. In contrast, in superfluid4Hethe effect of dissipation is of minor importance. In both liquids the role of the compressibility of a fluid enhances significantly for the small critical nuclei, which have several interatomic distances and can provide us the nucleation rates sufficient for the experimental observation of the homogeneous cavitation in the quantum regime. ©1997 American Institute of Physics.