  Several properties of massive stars with large effects of rotation and
radiation are studied. We show that there are 2 roots for the equation giving
the rotational velocities at break-up: 1) The usual solution, which is shown to
apply when the Eddington ratio $\Gamma$ of the star is smaller than formally
0.639. 2) Above this value of $\Gamma$, there is a second root, inferior to the
first one, for the break-up velocity. This second solution tends to zero, when
$\Gamma$ tends towards 1. This second root results from the interplay of
radiation and rotation, and in particular from the reduction by rotation of the
effective mass in the local Eddington factor. The analysis made here should
hopefully clarify a recent debate between Langer (\cite{La97,La98}) and Glatzel
(\cite{Gla98}).
  The expression for the global mass loss-rates is a function of both $\Omega$
and $\Gamma$, and this may give raise to extreme mass loss-rates ($\Omega
\Gamma $-limit). In particular, for O-type stars, LBV stars, supergiants and
Wolf-Rayet stars, even slow rotation may dramatically enhance the mass loss
rates. Numerical examples in the range of 9 to 120 M$_{\odot}$ at various
$T_\mathrm{eff}$ are given.
