  The color superconductivity under flavor asymmetric conditions relevant to
the compact star phenomenology is studied within the Nambu-Jona-Lasinio model.
We focus on the effect of the deformation of the Fermi surfaces on the pairing
properties and the energy budget of the superconducting state. We find that at
finite flavor asymmetries the color superconducting BCS state is unstable
towards spontaneous quadrupole deformation of the Fermi surfaces of the $d$ and
$u$ quarks into ellipsoidal form. The ground state of the phase with deformed
Fermi surfaces corresponds to a superposition of prolate and oblate deformed
Fermi ellipsoids of $d$ and $u$ quarks.
