  The Landau-Zener transition in a two level system can be suppressed or
enhanced by coupling to an environment, depending on the temperature and the
environment spectral function. We consider the marginal spectral function, when
the dissipation effects are important for arbitrarily slow motion. Landau-Zener
transition rate demonstrates a non-trivial dependence of the on the ``bias'',
i. e. on the rate of the two energy levels relative motion. The Landau-Zener
transition is fully suppressed for the values of the bias below a threshold
bias set by the coupling strength. Above the threshold, the transition rate for
zero temperature is found using the instanton method. At finite temperature,
the Landau-Zener transition rate has a non-monotonic dependence on the coupling
strength, being suppressed at the strong coupling.
