  We study the competence between chiral symmetry restoration and two flavor
color superconductivity (2SC) using a relativistic quark model with covariant
nonlocal interactions. We consider two different nonlocal regulators: a
Gaussian regulator and a Lorentzian regulator. We find that although the phase
diagrams are qualitative similar to those obtained using models with local
interactions, in our case the superconducting gaps at medium values of the
chemical potential are larger. Consequently, we obtain that in that region the
critical temperatures for the disappearance of the 2SC phase might be of the
order of 100-120 MeV. We also find that for ratios of the quark-quark and
quark-antiquark couplings somewhat above the standard value 3/4, the end point
and triple point in the $T-\mu$ phase diagram meet and a phase where both the
chiral and diquark condensates are non-negligible appears.
