  We discuss the equilibrium conditions for a body made of two homogeneous
components separated by oblate spheroidal surfaces and in relative motion.
While exact solutions are not permitted for rigid rotation (unless a specific
ambient pressure), approximations can be obtained for configurations involving
a small confocal parameter. The problem then admits two families of solutions,
depending on the pressure along the common interface (constant or quadratic
with the cylindrical radius). We give in both cases the pressure and the
rotation rates as a function of the fractional radius, ellipticities and
mass-density jump. Various degrees of flattening are allowed but there are
severe limitations for global rotation, as already known from classical theory
(e.g. impossibility of confocal and coelliptical solutions, gradient of
ellipticity outward). States of relative rotation are much less constrained,
but these require a mass-density jump. This analytical approach compares
successfully with the numerical solutions obtained from the
Self-Consistent-Field method. Practical formula are derived in the limit of
small ellipticities appropriate for slowly-rotating star/planet interiors.
