  Some ultraluminous X-ray sources (ULXs) exhibit X-ray pulses, and their
central sources are thought to be neutron stars. It has also been suggested
that some are transient sources with Be-type donors. In this study, we use the
mass accretion model of a Be-type high mass X-ray binary (BeHMXB) to estimate
the conditions under which a giant X-ray burst caused by a BeHMXB exceeds the
Eddington luminosity. Moreover, we investigate the duration for which BeHMXBs
can be observed as transient ULXs with bursts above the Eddington luminosity
during binary evolutions. The results indicate that BeHMXBs could be ULXs for a
typical duration of approximately 1 Myr. Comparisons with nearby observed
BeHMXBs indicate that many binary systems have the potential to become ULXs
during their evolution. Particularly, a BeHMXB system tends to become a ULX
when the Be donor has a dense deccretion disc aligned with the orbital plane.
Because BeHMXBs are very common objects and a significant number of them can
become ULXs, we conclude that a reasonable fraction of the observed ULXs could
consist of evolved BeHMXBs.
