  We investigate the in-medium properties of hyperons and anti-hyperons in the
framework of the Non-Linear Derivative (NLD) model. We focus on the momentum
dependence of in-medium strangeness optical potentials. The NLD model is based
on the simplicity of the well-established Relativistic Mean-Field (RMF)
approximation, but it incorporates an explicit momentum dependence on a
field-theoretical level. The extension of the NLD model to the
(anti)baryon-octet is formulated in the spirit of SU(6) and G-parity arguments.
It is shown that with an appropriate choice of momentum cut-offs the $\Lambda$,
$\Sigma$ and $\Xi$ optical potentials are consistent with recent studies of the
chiral effective field theory and Lattice-QCD calculations over a wide momentum
region. In addition, we present NLD predictions for the in-medium momentum
dependence of $\overline{\Lambda}$-, $\overline{\Sigma}$- and
$\overline{\Xi}$-hyperons. This work is important for future experimental
studies such as CBM, PANDA at the Facility for Antiproton and Ion Research
(FAIR). It is relevant for nuclear astrophysics too.
