  The Be X-ray pulsar (BeXRP) SXP 59 underwent a giant outburst in 2017 with a
peak X-ray luminosity of $1.1\times10^{38}$ erg~s$^{-1}$. We report on the
X-ray behaviour of SXP 59 with the XMM--Newton and NuSTAR observations
collected at the outburst peak, decay, and the low luminosity states. The pulse
profiles are energy dependent, the pulse fraction increases with the photon
energy and saturates at $\sim$ 65% above 10 keV. It is difficult to constrain
the change in the geometry of emitting region with the limited data.
Nevertheless, because the pulse shape generally has a double-peaked profile at
high luminosity and a single peak profile at low luminosity, we prefer the
scenario that the source transited from the super-critical state to the
sub-critical regime. This result would further imply that the neutron star (NS)
in SXP 59 has a typical magnetic field. We confirm that the soft excess
revealed below 2 keV is dominated by a cool thermal component. On the other
hand, the NuSTAR spectra can be described as a combination of the non-thermal
component from the accretion column, a hot blackbody emission, and an iron
emission line. The temperature of the hot thermal component decreases with
time, while its size remains constant ($R \sim 0.6$ km). The existence of the
hot blackbody at high luminosity cannot be explained with the present accretion
theories for BeXRPs. It means that either more sophisticated spectral models
are required to describe the X-ray spectra of luminous BeXRPs, or there is
non-dipole magnetic field close to the NS surface.
