  Two approaches to treat the chemical freeze-out of strange particles in
hadron resonance gas model are analyzed. The first one employs their
non-equillibration via the usual \gamma_s factor and such a model describes the
hadron multiplicities measured in nucleus-nucleus collisions at AGS, SPS and
RHIC energies with \chi^2/dof = 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 \chi^2/dof = 1.06. Remarkably, the fully equilibrated approach describes
the strange hyperons and antihyperons much better than the conventional one.
