  We formulate new general-relativistic extensions of Newtonian rotation laws
for self-gravitating stationary fluids. They have been used to re-derive, in
the first post-Newtonian approximation, the well known geometric dragging of
frames. We derive two other general-relativistic weak-field effects within
rotating tori: the recently discovered dynamic anti-dragging and a new effect
that measures the deviation from the Keplerian motion and/or the contribution
of the fluids selfgravity. One can use the rotation laws to study the
uniqueness and the convergence of the post-Newtonian approximations, and the
existence of the post-Newtonian limits.
