By solving the linearized Vlasov-Boltzmann equation it is shown that zero sound can exist in classical liquids. The effective interatomic potential is shown to be expressed in terms of the direct correlation function. The real and imaginary parts of the frequency are expressed analytically for both small and large values of wave-vector k, but in general are obtained numerically. In our solution of the dispersion relation, first (ordinary) sound and zero sound originate from the same pole; the former is the solution for smaller k and the latter is that for large k. We believe that the collective modes observed in classical liquids by neutron scattering experiments should be interpreted as zero sound. The imaginary part of the diffusion pole which contributes to the line width of the quasi-elastic peak, becomes small for the wave-vector where the form factor S(k) has peaks.