  We calculate the relativistic entrainment matrix Y_ik at zero temperature for
nucleon-hyperon mixture composed of neutrons, protons, Lambda and Sigma^-
hyperons, as well as of electrons and muons. This matrix is analogous to the
entrainment matrix (also termed mass-density matrix or Andreev-Bashkin matrix)
of non-relativistic theory. It is an important ingredient for modelling the
pulsations of massive neutron stars with superfluid nucleon-hyperon cores. The
calculation is done in the frame of the relativistic Landau Fermi-liquid theory
generalized to the case of superfluid mixtures; the matrix Y_ik is expressed
through the Landau parameters of nucleon-hyperon matter. The results are
illustrated with a particular example of the sigma-omega-rho mean-field model
with scalar self-interactions. Using this model we calculate the matrix Y_ik
and the Landau parameters. We also analyze stability of the ground state of
nucleon-hyperon matter with respect to small perturbations.
