  To elucidate the intrinsic nature of anomalous Hall effect (AHE) in
$d$-electron systems, we study the AC anomalous Hall conductivity (AHC) in a
tight-binding model with ($d_{xz},d_{yz}$)-orbitals. We drive a general
expression for the AC AHC $\sigma_{xy}(\omega)$, which is valid for finite
quasiparticle damping rate $\gamma$=$\hbar/2\tau$, and find that the AC AHC is
strongly dependent on $\gamma$. When $\gamma=+0$, the AC AHC shows a spiky peak
at finite energy $\Delta$ that originates from the interband particle-hole
excitation, where $\Delta$ represents the minimum band-splitting measured from
the Fermi level. In contrast, we find that this spiky peak is quickly
suppressed when $\gamma$ is finite. By using a realistic value of
$\gamma(\omega)$ at $\omega=\Delta/2$ in $d$-electron systems, the spiky peak
is considerably suppressed. In the present model, the obtained results also
represents the AC spin Hall conductivity in a paramagnetic state.
