  The charmed strange baryon Xi_c^0 was searched for in the decay channel
Xi_c^0 -> Xi- pi+, and the beauty strange baryon Xi_b in the inclusive channel
Xi_b -> Xi- l- anti-nu X, using the 3.5 million hadronic Z events collected by
the DELPHI experiment in the years 1992--1995. The Xi- was reconstructed
through the decay Xi- -> Lambda pi-, using a constrained fit method for cascade
decays. An iterative discriminant analysis was used for the Xi_c^0 and Xi_b
selection. The production rates were measured to be f_{Xi_c^0} x BR(Xi_c^0 ->
Xi- pi+)= (4.7 +/- 1.4 (stat.) +/- 1.1 (syst.))10^{-4} per hadronic Z decay,
and BR(b -> Xi_b) x BR(Xi_b -> Xi- l- X)= (3.0 +/- 1.0 (stat.) +/- 0.3
(syst.))10^{-4} for each lepton species (electron or muon). The lifetime of the
Xi_b baryon was measured to be tau_{Xi_b} = 1.45{^{+0.55}_{-0.43}} (stat.) +/-
0.13 (syst.) ps. A combination with the previous DELPHI lifetime measurement
gives tau_{Xi_b} = 1.48{^{+0.40}_{-0.31}} (stat.) +/- 0.12 (syst.) ps.
