  We report on BeppoSAX and Chandra observations of three Hard X-Ray Transients
in quiescence containing fast spinning (P<5 s) neutron stars: A 0538-66, 4U
0115+63 and V 0332+53. These observations allowed us to study these transients
at the faintest flux levels thus far. Spectra are remarkably different from the
ones obtained at luminosities a factor >10 higher, testifying that the
quiescent emission mechanism is different. Pulsations were not detected in any
of the sources, indicating that accretion of matter down to the neutron star
surface has ceased. We conclude that the quiescent emission of the three X-ray
transients likely originates from accretion onto the magnetospheric boundary in
the propeller regime and/or from deep crustal heating resulting from
pycnonuclear reactions during the outbursts.
