  Systematic ac susceptibility measurements have been performed on a MgB$_2$
bulk sample. We demonstrate that the flux creep activation energy is a
nonlinear function of the current density $U(j)\propto j^{-0.2}$, indicating a
nonlogarithmic relaxation of the current density in this material. The
dependence of the activation energy on the magnetic field is determined to be a
power law $U(B)\propto B^{-1.33}$, showing a steep decline in the activation
energy with the magnetic field, which accounts for the steep drop in the
critical current density with magnetic field that is observed in MgB$_2$. The
irreversibility field is also found to be rather low, therefore, the pinning
properties of this new material will need to be enhanced for practical
applications.
