Abstract A study of the collective motions of nuclear matter has been made. We first give a purely classical macroscopic description of hydrodynamic waves in nuclear matter, and suggest some experimental consequences of their excitation. Next a quantum mechanical study of the collective eigenstates of nuclear matter is taken up. The starting point of this discussion is the theory of the nuclear ground state as given by Brueckner and his collaborators. The excited states are described by means of the method developed by Sawada to apply to an electron gas. We generalize this method so as to include the internal degrees of freedom associated with spin and i-spin and to handle the momentum dependence of the level-shift operator K used by Brueckner. The connection between the quantum-mechanical eigenstates and the classical hydrodynamic motion is established. As a consequence of the internal degrees of freedom, there exist not only the usual compressive waves, but spin, i-spin, and coupled spin-i-spin waves. The i-spin waves can be associated with the Goldhaber-Teller oscillations. We have investigated the corrections to the Sawada theory. This gives rise to the damping of the stable Sawada collective eigenmodes, analogous to the viscous damping of a plasma oscillation. The spin and i-spin waves are only slightly damped, whereas the compressional mode is unstable in an exponentially growing sense.