AbstractThe production of $Ξ (1321)^{-}$ Ξ ( 1321 ) - and $\overline{\Xi }(1321)^{+}$ Ξ ¯ ( 1321 ) + hyperons in inelastic p+p interactions is studied in a fixed target experiment at a beam momentum of 158 $\hbox {Ge}\hbox {V}\!/\!c$ Ge / c . Double differential distributions in rapidity ${y}$ y and transverse momentum $p_{T}$ p T are obtained from a sample of 33M inelastic events. They allow to extrapolate the spectra to full phase space and to determine the mean multiplicity of both ${Ξ }{^-} $ Ξ - and $\overline{\Xi }{^+} $ Ξ ¯ + . The rapidity and transverse momentum spectra are compared to transport model predictions. The ${Ξ }{^-} $ Ξ - mean multiplicity in inelastic p+p interactions at 158 $\hbox {Ge}\hbox {V}\!/\!c$ Ge / c is used to quantify the strangeness enhancement in A+A collisions at the same centre-of-mass energy per nucleon pair.