  Robinson-Wilczek's recent work shows that, the energy momentum tensor flux
required to cancel gravitational anomaly at the event horizon of a
Schwarzschild-type black hole has an equivalent form to that of a
(1+1)-dimensional blackbody radiation at the Hawking temperature. Motivated by
their work, Hawking radiation from the cosmological horizons of the general
Schwarzschild-de Sitter and Kerr-de Sitter black holes, has been studied by the
method of anomaly cancellation. The result shows that the absorbing gauge
current and energy momentum tensor fluxes required to cancel gauge and
gravitational anomalies at the cosmological horizon are precisely equal to
those of Hawking radiation from it. It should be emphasized that the effective
field theory for generic black holes in de Sitter spaces should be formulated
within the region between the event horizon (EH) and the cosmological horizon
(CH), to integrate out the classically irrelevant ingoing modes at the EH and
the classically irrelevant outgoing modes at the CH, respectively.
