  We consider the Rayleigh-Taylor instability in the early evolution of the
rarefied radio bubbles (cavities) observed in many cooling flow clusters of
galaxies. The top of a bubble becomes prone to the Rayleigh-Taylor instability
as the bubble rises through the intra-cluster medium (ICM). We show that while
the jet is powering the inflation, the deceleration of the bubble-ICM interface
is able to reverse the Rayleigh-Taylor instability criterion. In addition, the
inflation introduces a drag effect which increases substantially the
instability growth time. The combined action of these two effects considerably
delays the onset of the instability. Later on, when the magnitude of the
deceleration drops or the jet fades, the Rayleigh-Taylor and the
Kelvin-Helmholtz instabilities set in and eventually disrupt the bubble. We
conclude that the initial deceleration and drag, albeit unable to prevent the
disruption of a bubble, may significantly lengthen its lifetime, removing the
need to invoke stabilising magnetic fields.
