In the collapse of a spherical cavity surrounded by a perfect gas initially at rest, the velocityR˙ of the free gas boundary has an initial valve of −2c0/(&ggr;−1) (c0is the speed of sound in the undisturbed gas and &ggr; is the adiabatic exponent). HereafterR˙ remains practically constant untilRbecomes a certain fraction &xgr;(&ggr;) of the initial radiusR0. Finally, forR<&xgr;R0,R˙ approaches the asymptotic behaviorR˙∼R−&tgr;(&ggr;)predicted by self‐similar solutions. The function &xgr;(&ggr;), which has been obtained numerically, decreases as &ggr; decreases and vanishes for a certain value of &ggr; near 1.5. This fact, together with the analogous behavior of &tgr;(&ggr;), suggests that there exists a certain value &ggr;cr≊1.5 of the adiabatic exponent such that, for 1<&ggr;<&ggr;crthe velocityR˙ of the free boundary is strictly a constant during the entire collapse. This behavior seems to be closely related to the results obtained by Lazarus [Phys. Fluids25, 1146 (1982)] who demonstrates that a degenerate stable, asymptotic solution, withR˙=const, exists for &ggr;<3/2.