  We investigate dynamics of Josephson vortex lattice in layered high T$_{c}$
superconductors at high magnetic fields. It is shown that the average electric
current depends on the lattice structure and is resonantly enhanced when the
Josephson frequency matches the frequency of the plasma mode. We find the
stability regions of moving lattice. It is shown that a specific lattice
structure at given velocity is uniquely selected by the boundary conditions: at
small velocities periodic triangular lattice is stable and looses its stability
at some critical velocity. At even higher velocities a structure close to a
rectangular lattice is restored.
