A convolution-type equation has been derived to describe the behavior of a bubble under periodical pressure oscillations. This equation holds for a diffusion-controlled adsorption mechanism and small disturbances of the equilibrium state, and it describes both the established and transition regimes of bubble oscillation. Systems free of any surfactant and in the presence of a surfactant are considered. The results obtained allow all aspects of surfactant influence on the bubble oscillation resonance to be analyzed. The sharp increase in the bubble oscillation amplitude may result in bubble detachments, even at rather low harmonic pressure oscillations. The presence of surfactant can result in a depression of the resonance amplitudes. Copyright 2000 Academic Press.