The earlier theory of the growth of vapor bubbles in superheated liquids is extended to the situation in which the rate of temperature rise of the liquid is large. Numerical solutions are presented for the early stages of bubble growth for various rates of liquid temperature rise. The asymptotic behavior of a bubble is found explicitly for a temperature rise of the liquid which is linear in time. In this case the bubble radius grows initially ast½, as in asymptotic solutions found previously for small rates of temperature rise, but then deviates toward a latet32variation.