There exist several proposals to use Weizsacker-Williams photons generated
by ultrarelativistic heavy ions to produce exotic particles in gamma gamma
fusion reactions. To estimate the background conditions for such reactions
we analyze various mechanisms of meson production in very peripheral collis
ions of ultrarelativistic heavy ions at RHIC and LHC energies. Besides the
gamma gamma fusion they include also electromagnetic gammaA interactions an
d strong nucleon-nucleon interactions in grazing AA collisions. All these p
rocesses are characterised by low multiplicities of produced particles. The
gammaA and AA events are simulated by corresponding Monte Carlo codes, REL
DIS and FRITIOF. In each of these processes a certain fraction of pions is
produced close to the mid-rapidity region that gives a background for the g
amma gamma events. The possibility of selecting the mesons produced in the
gamma gamma fusion events via different p(t) cut procedures is demonstrated
.