  X-ray spectra of groups of galaxies, obtained with the GIS instrument onboard
ASCA, were investigated for diffuse hard X-rays in excess of the soft thermal
emission from their inter-galactic medium (IGM). In total, 18 objects with the
IGM temperature of 0.7--1.7 keV were studied, including HCG 62 in particular.
Non X-ray backgrounds in the GIS spectra were carefully estimated and
subtracted. The IGM emission was represented by up to two temperature thermal
models, which was determined in a soft energy band below 2.5 keV mainly by the
SIS data. When extrapolated to a higher energy range of 4--8 keV, this thermal
model under-predicted the background-subtracted GIS counts in HCG 62 and RGH 80
by > 2 sigma significance, even though the background uncertainties and the IGM
modeling errors are carefully accounted. A hard excess could be also present in
NGC 1399. The excess was successfully explained by a power-law model with a
photon index ~ 2, or a thermal emission with a temperature exceeding ~ 3 keV.
In HCG 62, the 2--10 keV luminosity of the excess hard component was found to
be 5.5E41 erg/s at 2--10 keV, which is ~ 30% of the thermal IGM luminosity in
0.7--2.5 keV. Non-thermal and thermal interpretations of this excess components
are discussed.
