  We study the photoproduction of exclusive $2\pi^+2\pi^-$ mesons in
ultra-peripheral heavy-ion collisions at RHIC and LHC energies. Predictions in
photon-nucleus interactions are calculated for various resonances at central
and forward rapidities. The recent H1 preliminary data are utilized to improve
the description of the poorly known $\gamma p \to 4\pi^\pm p$ process. We
present the comparisons of our results to the available STAR data at RHIC, and
made predictions for LHC energies.
