  Ultra-luminous X-ray sources (ULXs) are off-nuclear point sources in nearby
galaxies with luminosities well exceeding the Eddington limit for stellar-mass
objects. It has been recognized after the discovery of pulsating ULXs (PULXs)
that a fraction of these sources could be accreting neutron stars in high-mass
X-ray binaries (HMXBs) though the majority of ULXs are lacking in coherent
pulsations. The earliest stage of some HMXBs may harbor rapidly rotating
neutron stars propelling out the matter transferred by the massive companion.
The spin-down power transferred by the neutron-star magnetosphere to the
accretion disk at this stage can well exceed the Eddington luminosities and the
system appears as a non-pulsating ULX. In this picture, PULXs appear as
super-critical mass-accreting descendants of non-pulsating ULXs. We present
this evolutionary scenario within a self-consistent model of magnetosphere-disk
interaction and discuss the implications of our results on the spin and
magnetic field of the neutron star.
