Plesset and Zwick [M. S. Plesset and S. A. Zwick, J. Appl. Phys.23, 95–98 (1952);25, 493–500 (1954); J. Math. Phys.33, 308–330 (1955)] have calculated the rate of growth of vapor bubbles in slightly superheated steam under constant external pressure. Their calculation assumes that the temperature drop is localized in a thin ``boundary layer'' near the bubble wall; the predicted bubble radiusR(t) is asymptotically proportional tot1/2whenRis large enough for surface tension to be negligible. An analysis of this asymptotic phase is given, which avoids the above ``boundary layer'' assumption, and contains that part of the analysis of Plesset and Zwick dealing with this phase as a limiting case. The analysis is shown to be (approximately) applicable also to gas bubbles in supersaturated liquids.