Tunneling phenomena occurring in potentials with several minima are di
scussed using a generalization of Landau's approach. In particular, th
e strong influence of the shape of the potential on the tunneling prob
abilities (resonances) and on the shape of a time-dependent wave packe
t (coherence) is shown for the case of the asymetric double square-wel
l potential. Finally, these features are illustrated for more realisti
c potentials by numerically solving the time-dependent Schrodinger equ
ation in one and two dimensions.