The condensation process in supersaturated vapors is analyzed with the help of thermodynamics and kinetic theory. The simplifying approximations which make the problem tractable are carefully examined. Results are obtained for the steady rate of condensation which constitute a theoretical improvement over Becker and Doring's values. The uncertainties in the values of the free energy for very small droplets, which are only partially removed by Tolman's theory on the variation of surface tension with curvature, limit this improvement in the condensation theory. Nonsteady condensation situations are also treated in detail by means of numerical and graphical integrations. It is found that the condensation in such situations generally approaches a steady rate in time periods of the order of 1 to 100 microseconds. Such time periods are negligible in many physical situations, but may be significant in the case of condensation shocks in wind tunnels. A similar analysis is carried out for the boiling of superheated liquids and the rupture of liquids under tension. Approximations reduce the analysis of these processes to mathematical relations very similar to those for the condensation process. Nonsteady solutions are obtained by numerical integration. It is found that the solutions ordinarily approach a steady rate of bubble formation in less than a microsecond.