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We consider transport properties of the hypernuclear matter in neutron starcores. In particular, we calculate the thermal conductivity, the shearviscosity, and the momentum transfer rates for np$\Sigma^{-}\Lambda e\mu$composition of dense matter in $\beta$--equilibrium for baryon number densitiesin the range $0.1-1$~fm$^{-3}$. The calculations are based on baryoninteractions treated within the framework of the non-relativisticBrueckner-Hartree-Fock theory. Bare nucleon-nucleon (NN) interactions aredescribed by the Argonne v18 phenomenological potential supplemented with theUrbana IX three-nucleon force. Nucleon-hyperon (NY) and hyperon-hyperon (YY)interactions are based on the \new{NSC97e and NSC97a models} of the Nijmegengroup. We find that the baryon contribution to transport coefficients isdominated by the neutron one as in the case of neutron star cores containingonly nucleons. In particular, we find that neutrons dominate the total thermalconductivity over the whole range of densities explored and that, due to theonset of $\Sigma^-$ which leads to the deleptonization of the neutron starcore, they dominate also the shear viscosity in the high density region, incontrast with the pure nucleonic case where the lepton contribution is alwaysthe dominant one.

Transport coefficients of hyperonic neutron star cores