  In this paper, collective excitations in a homogeneous fermion-fermion
mixture with different Fermi surfaces are studied. In the Fermi liquid phase,
the zero-sound velocity is found to be larger than the largest Fermi velocity.
With attractive interactions, the superfluid phase appears below a critical
temperature, and the phase mode is the low-energy collective excitation. The
velocity of the phase mode is proportional to the geometric mean of the two
Fermi velocities. The difference between the two velocities may serve as a tool
to detect the superfluid phase.
