  The nonadiabatic transition probabilities in the two-level systems are
calculated analytically by using the monodromy matrix determining the global
feature of the underlying differential equation. We study the time-dependent
2x2 Hamiltonian with the tanh-type plus sech-type energy difference and with
constant off-diagonal elements as an example to show the efficiency of the
monodromy approach. The application of this method to multi-level systems is
also discussed.
