In experiments of capillary rise, oscillations of the liquid column can occur, as recently reported for liquids of low viscosity (Europhys. Lett. 1997, 39, 533). Here we analyze these oscillations (criterion of existence, shape, and damping). We start with an ideal fluid for which the oscillations are found to be indefinite and parabolic. Then, we take into account the dissipation at the entrance of the pipe: it is shown that it implies a different equation of motion depending on the direction of the liquid column (rise or fall). The first rise remains of parabolic shape, but a dissymmetry is found between this rise and the fall. Finally, the classical viscous friction inside the pipe is incorporated in the description and shown to accelerate the damping.