  Recently, Hawking radiation from a Schwarzschild-type black hole via
gravitational anomaly at the horizon has been derived by Robinson and Wilczek.
Their result shows that, in order to demand general coordinate covariance at
the quantum level to hold in the effective theory, the flux of the energy
momentum tensor required to cancel gravitational anomaly at the horizon of the
black hole, is exactly equal to that of (1+1)-dimensional blackbody radiation
at the Hawking temperature. In this paper, we attempt to apply the analysis to
derive Hawking radiation from the event horizons of static, spherically
symmetric dilatonic black holes with arbitrarily coupling constant $\alpha$,
and that from the rotating Kaluza-Klein $(\alpha = \sqrt{3})$ as well as the
Kerr-Sen ($\alpha = 1$) black holes via an anomalous point of view. Our results
support Robinson-Wilczek's opinion. In addition, the properties of the obtained
physical quantities near the extreme limit are qualitatively discussed.
