Supergiant Fast X–ray Transients ( SFXTs ) are a new class of High Mass X–ray Binaries ( HMXBs ) discovered thanks to the monitoring of the Galactic plane performed with the INTEGRAL satellite in the last 5 years . These sources display short outbursts ( significantly shorter than typical Be/X-ray binaries ) with a peak luminosity of a few 10 ^ { 36 } erg s ^ { -1 } . The quiescent level , measured only in a few sources , is around 10 ^ { 32 } erg s ^ { -1 } . The X–ray spectral properties are reminiscent of those of accreting pulsars , thus it is likely that all the members of the new class are indeed HMXBs hosting a neutron star , although only two SFXTs have a measured pulse period , IGR J11215–5952 ( \sim 187 s ) and IGR J18410 - 0535 ( \sim 4.7 s ) . Several competing mechanisms have been proposed to explain the shortness of these outbursts , mostly involving the structure of the wind from the supergiant companion . To characterize the properties of these sources on timescales of months ( e.g . the quiescent level and the outburst recurrence ) , we are performing a monitoring campaign with Swift of four SFXTs ( IGR J16479 - 4514 , XTE J1739 - 302 , IGR J17544 - 2619 and AX J1841.0 - 0536/IGR J18410 - 0535 ) . We report on the first four months of Swift observations , started on 2007 October 26 . We detect a low level X–ray activity in all four SFXTs which demonstrates that these transient sources accrete matter even outside their outbursts . This fainter X–ray activity is composed of many flares with a large flux variability , on timescales of thousands of seconds . The lightcurve variability is also evident on larger timescales of days , weeks and months , with a dynamic range of more than one order of magnitude in all four SFXTs . The X–ray spectra are typically hard , with an average 2–10 keV luminosity during this monitoring of about 10 ^ { 33 } –10 ^ { 34 } erg s ^ { -1 } . We detected pulsations from the pulsar AX J1841.0 - 0536/IGR J18410 - 0535 , with a period of 4.7008 \pm { 0.0004 } s. This monitoring demonstrates that these transients spend most of the time accreting matter , although at a much lower level ( \sim 100–1000 times lower ) than during the bright outbusts , and that the “ true quiescence ” , characterized by a soft spectrum and a luminosity of a few 10 ^ { 32 } erg s ^ { -1 } , observed in the past only in a couple of members of this class , is probably a very rare state .