ROSAT observations of A0538--66 during quiescence

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".