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 significantly different from the zero-sound velocity. The difference between the two velocities may serve as a tool to detect the superfluid phase.