  We compute models for the equation of state (EoS) of the matter in the cores
of hybrid stars. Hadronic matter is treated in the non-linear relativistic
mean-field approximation, and quark matter is modeled by three-flavor local and
non-local Nambu$-$Jona-Lasinio (NJL) models with repulsive vector interactions.
The transition from hadronic to quark matter is constructed by considering
either a soft phase transition (Gibbs construction) or a sharp phase transition
(Maxwell construction). We find that high-mass neutron stars with masses up to
$2.1-2.4 M_\odot$ may contain a mixed phase with hadrons and quarks in their
cores, if global charge conservation is imposed via the Gibbs conditions.
However, if the Maxwell conditions is considered, the appearance of a pure
quark matter core either destabilizes the star immediately (commonly for
non-local NJL models) or leads to a very short hybrid star branch in the
mass-radius relation (generally for local NJL models).
