The dynamics of the sinusoidally driven cavitation bubble oscillator influenced by external random signals, modelled by white noise and an Ornstein-Uhlenbeck process, is studied. By numerical simulations it is shown that chaotic oscillations of cavitation bubble oscillators can be stabilized to periodic oscillations. Shift of bifurcation points and destruction of period-doubling cascades were observed as a result of the action of noise. They are discussed from the point of view of experimental time series. ©2000 American Institute of Physics.