Based on the two-fluid hydrodynamics, an analog of the famous Rayleigh-Plesset equation for the dynamics of a spherical vapor bubble in superfluid helium is derived. The two-fluid nature of He II and the specific form of the momentum flux density tensor give rise to a number of effects in the evolution of the boundary position R(t), absent in ordinary fluids. One of them is the abnormal attenuation of the boundary oscillation, which exceeds the usual viscous damping by several orders of magnitude. There is also an additional term proportional to the squared velocity of the normal component, which is independent of the derivative dR/dt, and therefore can be included in the pressure drop. Its physical meaning is related to the dependence of pressure on the relative velocity between the normal and superfluid components. One more effect renormalizes the coefficient in front of (dR/dt)2. The dissipative part of the momentum flux tensor is also being upgraded to take into account the two-fluid hydrodynamics. As an illustration of the stated theory, a numerical solution of the obtained master equation for the evolution of a vapor film on spherical heaters in He II is presented. The obtained results declare that some early issues and conclusions on the dynamics of the cavity in superfluid helium should be reviewed.