  We study the coherent dynamics of a Holstein polaron in strong electric
fields. A detailed analytical and numerical analysis shows that even for small
hopping constant and weak electron-phonon interaction, polaron states can
become delocalized if a resonance condition develops between the original
Wannier-Stark states and the phonon modes, yielding both tunneling and
`stretched' polarons. The unusual stretched polarons are characterized by a
phonon cloud that {\em trails} the electron, instead of accompanying it. In
general, our novel approach allows us to show that the polaron spectrum has a
complex nearly-fractal structure, due to the coherent coupling between states
in the Cayley tree which describes the relevant Hilbert space. The eigenstates
of a finite ladder are analyzed in terms of the observable tunneling and
optical properties of the system.
