  We disuss exclusive electromagnetic production of two neutral $\rho^0$~mesons
and show the predictions for the $AA \to AA \rho^0 \rho^0$ reactions for
gold-gold collisions at the energy of $\sqrt{s}$ = 200 GeV (RHIC) and for
lead-lead collisions at the energy of $\sqrt{s}$ = 5.5 TeV (LHC). The
elementary cross section is calculated with the help of the
vector-dominance-model (VDM)-Regge approach which usually very well describes
the experimental data at large $\gamma \gamma$ energy. The low-energy $\gamma
\gamma \to \rho^0 \rho^0$ cross section is parametrized. The cross section for
nuclear process is calculated by means of the equivalent photon approximation
(EPA). We compare the results with realistic charge density with the results
for monopole form factor.
