  We estimate the cross sections for the production of resonances, pion pairs
and a central cluster of hadrons in peripheral heavy-ion collisions through
two-photon and double-pomeron exchange, at energies that will be available at
RHIC and LHC. The effect of the impact parameter in the diffractive reactions
is introduced, and imposing the condition for realistic peripheral collisions
we verify that in the case of very heavy ions the pomeron-pomeron contribution
is indeed smaller than the electromagnetic one. However, they give a
non-negligible background in the collision of light ions. This diffractive
background will be more important at RHIC than at LHC.
