From an observational point of view the phase-space structures of the Milky Way velocity field can reflect the correlations predicted in these models. Stimulated by our results concerning gravitational dynamics we have studied the kinematic structure of the Milky Way and of external galaxies.  It is usually assumed that the stars of our Galaxy should revolve around the central nucleus in a manner similar to how the planets revolve around the Sun, that is, with a rotating motion in which there is a balance between centrifugal and centripetal force. The dynamic equilibrium that is established allows to relate the rotation speed to the mass of the galaxy: this is the basis of the estimates of dark matter. We have tried to test this hypothesis both in our galaxy and in external ones.