  AX J0049.4-7323 is a Be/X-ray binary in the Small Magellanic Cloud hosting a
~750 s pulsar which has been observed over the last ~17 years by several X-ray
telescopes. Despite numerous observations, little is known about its X-ray
behaviour. Therefore, we coherently analysed archival Swift, Chandra,
XMM-Newton, RXTE, and INTEGRAL data, and we compared them with already
published ASCA data, to study its X-ray long-term spectral and flux
variability. AX J0049.4-7323 shows a high X-ray variability, spanning more than
three orders of magnitudes, from L ~ 1.6E37 erg/s (0.3-8 keV, d=62 kpc) down to
L ~ 8E33 erg/s. RXTE, Chandra, Swift, and ASCA observed, in addition to the
expected enhancement of X-ray luminosity at periastron, flux variations by a
factor of ~ 270 with peak luminosities of ~2.1E36 erg/s far from periastron.
These properties are difficult to reconcile with the typical long-term
variability of Be/XRBs, traditionally interpreted in terms of type I and type
II outbursts. The study of AX J0049.4-7323 is complemented with a spectral
analysis of Swift, Chandra, and XMM-Newton data which showed a softening trend
when the emission becomes fainter, and an analysis of optical/UV data collected
by the UVOT telescope on board Swift. In addition, we measured a secular
spin-up rate of $\dot{P}=(-3.00\pm0.12)\times 10^{-3}$ s day$^{-1}$, which
suggests that the pulsar has not yet achieved its equilibrium period. Assuming
spherical accretion, we estimated an upper limit for the magnetic field
strength of the pulsar of ~3E12 G.
