  We present the first systematic broad-band X-ray study of super-Eddington
accretion onto SMBHs with simultaneous {\it NuSTAR} and {\it XMM-Newton} or
{\it Swift}/XRT observations of a sample of 8 super-Eddington accreting AGN
with Eddington ratio $1<\lambda_{\rm Edd}<426$. We find that the SEAMBHs show a
steep primary continuum slope as expected for sources accreting in the super
Eddington regime, mostly dominated by relativistic reflection. The Iron
K$\alpha$ emission lines of the sources of our sample show relativistic
broadening. In addition the equivalent widths of the narrow components of the
Iron K$\alpha$ lines follow the 'X-ray Baldwin' effect, also known as the
'Iwasawa-Taniguchi' effect. We found a statistically significant correlation
between the photon-index of the primary power-law and the Eddington ratio,
consistent with past studies. Moreover, as expected for super-Eddington
sources, the median value of the reflection fraction of the sources we analysed
is a factor $\sim 2$ higher than the median reflection fraction value of the
type\,1 AGN from the BASS sample. We are able to estimate the coronal
temperature for three sources of our sample: Mrk\,382 ($kT_e=7.8$\,keV),
PG\,0026+129 ($kT_e=39$\,keV) and IRAS\,04416+1215 ($kT_e=3$\,keV). Looking at
the position of the SEAMBHs sources of our sample in the
compactness-temperature diagram it appears that in super-Eddington AGN, as for
lower Eddington ratio AGN, the X-ray corona is controlled by pair production
and annihilation.
