Zener's treatment of the tunneling process between two crossing diabatic levels is generalized to include time effects, as well as time dependence of the participating levels and their intercoupling. All of these can affect in a significant way the various transition probabilities of interest. These generalizations are necessary if the Zener process is to serve a useful role in describing transitions in N-level systems. We find a possible nonmonotonic dependence of the transition probability on the rate of change of the external bias (e.g. a magnetic field). Power law corrections to the leading transition probability are shown to exist when finite time effects are included. Finally we wish to mention the possible saturation of the localization length in energy space as a function of the bias in a many-level system in the sudden limit.
