  The dynamics of magnetic field penetration into thin-walled superconducting
niobium cylinders is experimentally investigated. It is shown that magnetic
field penetrates through the wall of a cylinder in a series of giant jumps with
amplitude 10 - 20 Oe and duration of a few $\mu$s. The jumps take place when
the total current in the wall, not the current density, exceeds some critical
value. In addition there are small jumps and/or smooth penetration, and their
contribution can reach 20% of the total penetrating flux. It is demonstrated
that the magnetic field inside the cylinder exhibits several oscillations. The
number of giant jumps reduces with temperature.
