  The sharp peak in the K+/pi+ ratio in relativistic heavy-ion collisions is
discussed in the framework of the Statistical Model. In this model a rapid
change is expected as the hadronic gas undergoes a transition from a
baryon-dominated to a meson-dominated gas. The maximum in the Lambda/\pi$ ratio
is well reproduced by the Statistical Model, but the change in the K+/pi+ ratio
is somewhat less pronounced than the one observed by the NA49 collaboration.
The calculated smooth increase of the K-/pi ratio and the shape of the Xi-/pi+
and Omega-/pi+ ratios exhibiting maxima at different incident energies is
consistent with the presently available experimental data. We conclude that the
measured particle ratios with $20-30%$ deviations agree with a hadronic
freeze-out scenario. These deviations seem to occur just in the transition from
baryon-dominated to meson-dominated freeze-out.
