[en] Measurements of the production of singly and doubly strange particles in S+Pb collisions at a beam momentum of 200 GeV/c per nucleon are presented. The yield of single strange particles as a function of negative particle multiplicity has been measured. Rapidity and transverse momentum distributions from events consistent with a maximum impact parameter of 9 fm are compared with the predictions of Fritiof 7.02, Venus 4.10 and RQMD 1.08. The comparison illustrates the importance of re-interactions of secondaries and suggests that additional physical processes are required to be incorporated into the event generators. The analysis of strange particle ratios indicates that strangeness phase space is not saturated in these collisions. (orig.)