A nonlinear problem of thermal, mass and dynamic interaction between a vapour-gas bubble and a liquid is considered with account for temperature nonuniformity in the bubble and interdiffusion of the vapour-gas mixture components. A numerical solution is obtained for the problem of radial bubble motion induced by a sudden pressure change in the liquid - a situation which, in particular, corresponds to the behaviour of bubbles beyond a shock-wave front when the latter enters a bubble curtain. Considered also are vapour-gas bubbles oscillating in the liquid under the influence of a sound field. The capillary effects and phase transitions, taken together, are shown to produce a new resonant frequency of small vapour bubbles which differs from that described by Minnaert. The expressions for the frequency and the thermal damping ratio of bubble oscillations are obtained. The effective coefficients of heat transfer between radially oscillating bubbles and the liquid are determined.