  The Hubbard-Holstein model is one of the simplest to incorporate both
electron-electron and electron-phonon interactions. In one dimension at half
filling the Holstein electron-phonon coupling promotes onsite pairs of
electrons and a Peierls charge density wave while the Hubbard onsite Coulomb
repulsion U promotes antiferromagnetic correlations and a Mott insulating
state. Recent numerical studies have found a possible third intermediate phase
between Peierls and Mott states. From direct calculations of charge and spin
susceptibilities, we show that (i) As the electron-phonon coupling is
increased, first a spin gap opens, followed by the Peierls transition. Between
these two transitions the metallic intermediate phase has a spin gap, no charge
gap, and properties similar to the negative-U Hubbard model. (ii) The
transitions between Mott/intermediate and intermediate/Peierls states are of
the Kosterlitz-Thouless form. (iii) For larger U the two transitions merge at a
tritical point into a single first order Mott/Peierls transition. In addition
we show that an intermediate phase also occurs in the quarter-filled model.
