  We have studied the magnetization and magnetoresistance of CeRu2Al10 in the
applied magnetic field H along the c-axis up to ~ 55 T. The magnetization M at
low temperatures shows an H-linear increase with a small slope of M/H than that
for H // a-axis up to ~ 55 T after showing a small anomaly at H ~ 4 T, which
indicates that the critical field to the paramagnetic phase H_c^p is higher
than 55 T for H // c-axis. The magnetization curves for H // a- and c-axes
below the antiferro magnetic (AFM) transition temperature T0 behave as if the
magnetic anisotropy in the AFM-ordered phase is small, although there exists a
large magnetic anisotropy in the paramagnetic phase, which favors the easy
magnetization axis along the a-axis. On the other hand, very recently,
Khalyavin et al. have reported that the AFM order where the magnetic moment is
parallel to the c-axis takes place below T0. These results indicate that the
AFM order in this compound is not a simple one. The longitudinal
magnetoresistance for H // c-axis at low temperatures shows no anomaly
originating from the phase transition, but shows oscillations below 4.2 K. This
oscillatory behavior below 4.2 K originates from the Shubnikov-de Haas
oscillations, from which the cross section of the Fermi surface normal to the
c-axis is estimated to be 1.0*10^14 cm-2, with no large effective mass. This is
the first direct evidence of the existence of the Fermi surface below T0.
