  Event-by-event fluctuations of the kaon to pion number ratio in
nucleus-nucleus collisions are studied within the statistical hadron-resonance
gas model (SM) for different statistical ensembles and in the
Hadron-String-Dynamics (HSD) transport approach. 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. Substantial differences in the HSD and SM results are found for the
fluctuations and correlations of the kaon and pion numbers. These predictions
impose a challenge for future experiments.
