  We discuss nuclear cross sections for $AA \to AAV$ and $AA \to AAVV$
reactions with one or two vector mesons in the final state. Our analysis is
done in the impact parameter space equivalent photon approximation. This
approach allows to consider the above processes taking into account distance
between colliding nuclei. We consider both ultraperipheral and semi-central
collisions. We are a first group which undertook a study of single $J/\psi$
photoproduction for different centrality bins. We show that one can describe
new ALICE experimental data by including geometrical effects of collisions in
the flux factor.
  Next, total and differential cross section for double-scattering mechanism in
the exclusive $AA \to AAVV$ reaction in ultrarelativistic ultraperipheral heavy
ion collisions is presented. In this context we consider double photoproduction
and photon-photon processes. Simultaneously, we get very good agreement of our
results with STAR (RHIC), CMS and ALICE (LHC) experimental data for single
$\rho^0$ and $J/\psi$ vector meson production. A comparison of our predictions
for exclusive four charged pions production is also presented.
