Abstract
For a fluid mass consisting of two conjocal sphcroids each one with different density, we demonstrate, ffrstly, the non-existence of equilibrium figures if both spheroids rotate with a common angular velocity and, secondly, the existence of equilibrium figures if they rotate with different angular velocities. The fluid is to be considered incompressible, self-gravitating, free from any external pressure and that each spheroid of the model is homogeneous per Se.
