We study the dewetting of liquid films deposited inside nonwettable and wettable capillaries. Two processes compete: (i) Rayleigh instability (i.e., amplification of thickness fluctuations) and (ii) dewetting by nucleation and growth of a dry zone limited by a rim collecting the liquid. At times shorter than the characteristic time tau(M) of the growth of the Rayleigh instability, we expect two regimes: (i) annular rims and drying at constant velocities and (ii) columnar rims with drying velocities decreasing versus time. For wettable capillaries, in a certain regime of thin thicknesses, the Rayleigh instability is absent and dewetting is the only process to remove the film.