  Nematic Fermi liquid arises when the system of interacting fermions
spontaneously breaks the rotational symmetry while the translational symmetry
is preserved. We consider a Nematic Fermi liquid of fermions with two distinct
quantum numbers. Two quantum numbers represent the spin degrees of freedom or
the layer degrees of freedom of the bilayer system. There are two director
modes in this system: the in-phase and out-of-phase modes. We find that the
out-of-phase (in-phase) mode mediates an attractive (repulsive) interaction
between fermions with different quantum numbers. Pairing instability occurs
under certain conditions when the in-phase mode is gapped due to a lattice
potential. Implications to the stripe phase of Cuprates and the quantum Hall
effect of two dimensional electron systems are discussed.
