  The phase diagram of charge and color neutral two-flavor color
superconducting quark matter is studied including the homogeneous two-flavor
superconductor (2SC) and the inhomogeneous Fulde-Ferrell (FF) phases within the
Nambu-Jona-Lasinio model. The low-temperature domain T < 5 MeV of the phase
diagram contains the FF phase, which borders at high temperatures to the 2SC
phase. The critical temperature of phase transition from the 2SC to the
unpaired state is in the range 20-30 MeV. We derive the equation of state of
matter and its composition and show that matter in mature compact stars should
be in the inhomogeneous FF-like superconducting state. We briefly discuss the
astrophysical implications of such a phase in compact stars.
