  We study nonmagnetic impurity effects in MgB$_{2}$ using the quasiclassical
equations of superconductivity for a weak-coupling two-band model. Parameters
in the model are fixed so as to reproduce experiments on MgB$_{2}$ as closely
as possible. The quasiparticle density of states and the specific heat are
calculated for various values of the interband impurity scattering. The density
of states changes gradually from a two-gap structure into the conventional
single-gap structure as the interband scattering increases. It is found that
the excitation threshold is not a monotonic function of the interband
scattering. Calculated results for the specific heat are in good agreements
with experiments on samples after irradiation.
