  We have observed the conduction electron spin resonance (CESR) in fine
powders of MgB2 both in the superconducting and normal states. The Pauli
susceptibility is chi_s=2.0*10^{-5} emu/mole in the temperature range of 450 to
600 K. The spin relaxation rate has an anomalous temperature dependence. The
CESR measured below T_c at several frequencies suggests that MgB_2 is a
strongly anisotropic superconductor with the upper critical field, H_c2,
ranging between 2 and 16 T. The high-field reversible magnetization data of a
randomly oriented powder sample are well described assuming that MgB_2 is an
anisotropic superconductor with H_c2^{ab} / H_{c2}^{c} \approx 6--9.
