  SAX J0635.2+0533 is a binary pulsar with a very short pulsation period ($P$ =
33.8 ms) and a high long-term spin down ($\dot P$ $>$ 3.8$\times10^{-13}$ s
s$^{-1}$), which suggests a rotation-powered (instead of an accretion-powered)
nature for this source. While it was discovered at a flux level around
10$^{-11}$ erg cm$^{-2}$ s$^{-1}$, between 2003 and 2004 this source was
detected with XMM-Newton at an average flux of about 10$^{-13}$ erg cm$^{-2}$
s$^{-1}$; moreover, the flux varied of over one order of magnitude on time
scales of a few days, sometimes decreasing below $3\times10^{-14}$ erg
cm$^{-2}$ s$^{-1}$. Since both the rotation-powered and the accretion-powered
scenarios have difficulties to explain these properties, the nature of SAX
J0635.2+0533 is still unclear. Here we report on our recent long-term
monitoring campaign on SAX J0635.2+0533 carried out with Swift and on a
systematic reanalysis of all the RXTE observations performed between 1999 and
2001. We found that during this time interval the source remained almost always
active at a flux level above 10$^{-12}$ erg cm$^{-2}$ s$^{-1}$.
