Chemical freeze-out of strange particles and possible root of strangeness suppression

Two approaches to treat the chemical freeze-out of strange particles in the hadron resonance gas model are analyzed. The first one employs their non-equillibration via the usual γs factor and such a model describes the hadron multiplicities measured in nucleus-nucleus collisions at AGS, SPS and RHIC energies with X2/dof [asymptotically =] 1.15. Surprisingly, at low energies we find not the strangeness suppression, but its enhancement. Also we suggest an alternative approach to treat the strange particle freeze-out separately, but with the full chemical equilibration. This approach is based on the conservation laws which allow us to connect the freeze-outs of strange and non-strange hadrons. Within the suggested approach the same set of hadron multiplicities can be described better than within the conventional approach with X2/dof [asymptotically =] 1.06.