  We develop a theory in order to describe the effect of relaxation in a
condensed medium upon the quantum decay of a metastable liquid near the
spinodal at low temperatures. We find that both the regime and the rate of
quantum nucleation strongly depend on the relaxation time and its temperature
behavior. The quantum nucleation rate slows down with the decrease of the
relaxation time. We also discuss the low temperature experiments on cavitation
in normal $^3$He and superfluid $^4$He at negative pressures. It is the sharp
distinctions in the high frequency sound mode and in the temperature behavior
of the relaxation time that make the quantum cavitation kinetics in $^3$He and
$^4$He completely different in kind.
