  During the adiabatic time evolution levels crossing violates the adiabaticity
and makes transitions between levels possible. Conventionally only two energy
levels cross simultaneously. The transition probabilities for this case were
found by Landau and Zener. However, the multilevel crossing happens
systematically rather than occasionally if the Hamiltonian possesses a special
symmetry. The simplest physical realization of the multilevel crossing are the
Zeeman multiplet in a varying magnetic field and an electron in one-dimensional
chain driven by the time-dependent electric field. We present asymptotics of
the transition amplitudes for these kinds of the multilevel crossing. They are
based on an exact solution for a model n-state, time-dependent Schr\"{o}dinger
equation.
