  The multiplicity fluctuations in A+A collisions at SPS and RHIC energies are
studied within the HSD transport approach. We find a dominant role of the
fluctuations in the nucleon participant number for the final fluctuations. In
order to extract physical fluctuations one should decrease the fluctuations in
the participants number. This can be done considering very central collisions.
The system size dependence of the multiplicity fluctuations in central A+A
collisions at the SPS energy range -- obtained in the HSD and UrQMD transport
models -- is presented. The results can be used as a `background' for
experimental measurements of fluctuations as a signal of the critical point.
Event-by-event fluctuations of the $K/\pi$, $K/p$ and $p/\pi$ ratios in A+A
collisions are also studied. Event-by-event fluctuations of the kaon to pion
number ratio in nucleus-nucleus collisions are studied for SPS and RHIC
energies. We find that the HSD model can qualitatively reproduce the measured
excitation function for the $K/\pi$ ratio fluctuations in central Au+Au (or
Pb+Pb) collisions from low SPS up to top RHIC energies. The forward-backward
correlation coefficient measured by the STAR Collaboration in Au+Au collisions
at RHIC is also studied. We discuss the effects of initial collision geometry
and centrality bin definition on correlations in nucleus-nucleus collisions. We
argue that a study of the dependence of correlations on the centrality bin
definition as well as the bin size may distinguish between these `trivial'
correlations and correlations arising from `new physics'.
