  Based on the definition of the apparent horizon in a general two-dimensional
dilaton gravity theory, we analyze the tunnelling phenomenon of the apparent
horizon by using Hamilton-Jacobi method. In this theory the definition of the
horizon is very different from those in higher-dimensional gravity theories.
The spectrum of the radiation is obtained and the temperature of the radiation
is read out from this spectrum and it satisfies the usual relationship with the
surface gravity. Besides, the calculation with Parikh's null geodesic method
for a simple example conforms to our result in general stationary cases.
