  The cross sections for the production of two-pions in ultraperipheral
ultrarelativistic heavy ion collisions, calculated in the impact parameter
Equivalent Photon Approximation (EPA), are presented. Differential
distributions in impact parameter, dipion invariant mass, single pion and
dipion rapidity, pion transverse momentum and pion pseudorapidity are shown.
The $\gamma \gamma \to \pi^+ \pi^-$ subprocess constitutes a background to the
$A A \to A \rho^0 (\to \pi^+ \pi^-) A$ process, initiated by emission of a
photon by one of colliding nuclei. Only a part of the dipion invariant mass
distribution associated with the $\gamma\gamma$-collisions can be visible as
the cross section for the $A A \to A \rho^0 A$ reaction is very large.
  Differential distributions for two $\rho^0$ meson production in exclusive
ultraperipheral, ultrarelativistic collisions via a double scattering mechanism
are presented. The cross section for $\gamma A \to \rho^0 A$ is parametrized
based on a calculation from the literature. Smearing of $\rho^0$ masses is
taken into account. The results of calculations are compared to experimental
data obtained at RHIC and to the contribution of the two-photon mechanism.
  The double scattering mechanism populates larger $\rho^0 \rho^0$ invariant
masses and larger rapidity distances between the two $\rho^0$ mesons compared
to the $\gamma \gamma$ fusion. It gives a significant contribution to the $A A
\to A A \pi^+ \pi^- \pi^+ \pi^-$ reaction. Some observables related to charged
pions are presented. The results of our calculation are compared with the STAR
collaboration results for four charged pion production. While the shape in
invariant mass of the four-pion system is very similar to the measured one, the
predicted cross section constitutes only 20 \% of the measured one.
\end{abstract}
