  We first review the production and the possible chemical equilibration of
strange particles at CERN-SPS energies within a microscopic hadronic transport
calculation. It is shown in particular that the strange quarks are produced
initially via string excitations in the primary, secondary and ternary
interactions. We then further elaborate on a recent idea of antihyperon
production by multi-mesonic reactions like $n_1\pi + n_2 K \to \bar{Y}+p $
corresponding to the inverse of the strong binary baryon-antibaryon
annihilation process. It is argued that by these reactions the (rare)
antihyperons are driven towards local chemical equilibrium with pions, nucleons
and kaons on a timescale of 1--3 fm/c in the still moderately baryon-dense
initial hadronic environment after the termination of the prehadronic string
phase. Accordingly this mechanism can provide a convenient explanation for the
antihyperon yields at CERN-SPS energies without any need of a deconfined quark
gluon plasma phase.
