  We discuss serendipitous ROSAT observations of the Be transient A0538-66,
which contains the fastest known accreting X-ray pulsar (69 ms). We show that
this transient is detected several times during quiescence at a level of about
10^34-35 erg/s. Considering this low luminosity it is more likely that X-rays
are produced by matter falling onto the neutron star magnetosphere, rather than
onto the star surface. This could be the first example of an X-ray source in
the "propeller regime".
