  Data on mean numbers of $\Lambda$, $\bar\Lambda$, K's and on the total number
$<s\bar s>$ of pairs of strange valence quarks in final state hadrons in
hadronic and nuclear collisions at CERN- SPS energies are studied as a function
of the mean number $<n_{coll}>$ of nucleon- nucleon collisions. Results give
indications of an almost linear dependence over most of the region of
$<n_{coll}>$. This in turn points out to strangeness being produced mostly in
the central rapidity region of nucleon- nucleon collisions by a mechanism
similar to a hard or semi- hard process. The available data are extrapolated to
Pb+Pb interactions by two simple models, leading to $<s\bar s>_{Pb+Pb}\approx
300\pm 30 $.
  Observations exceeding these values of $<s\bar s>_{Pb+Pb}$ would give
evidence of the onset of a new dynamical regime in Pb+Pb interactions.
