  We discuss a Nambu--Jona-Lasinio (NJL) type quantum field theoretical
approach to the quark matter equation of state with color superconductivity and
construct hybrid star models on this basis. It has recently been demonstrated
that with increasing baryon density, the different quark flavors may occur
sequentially, starting with down-quarks only, before the second light quark
flavor and at highest densities also the strange quark flavor appears. We find
that color superconducting phases are favorable over non-superconducting ones
which entails consequences for thermodynamic and transport properties of hybrid
star matter. In particular, for NJL-type models no strange quark matter phases
can occur in compact star interiors due to mechanical instability against
gravitational collapse, unless a sufficiently strong flavor mixing as provided
by the Kobayashi-Maskawa-'t Hooft determinant interaction is present in the
model. We discuss observational data on mass-radius relationships of compact
stars which can put constraints on the properties of dense matter equation of
state.
