We study a nonminimal massive scalar field in the background of a two-dimen
sional black hole spacetime. We consider the black hole which is the soluti
on of the 2D dilaton gravity derived from string-theoretical models. We fin
d an explicit solution in a closed form for all modes and the Green functio
n of the scalar field with an arbitrary mass and a nonminimal coupling to t
he curvature. Greybody factors, the Hawking radiation, and (phi (2))(ren) a
re calculated explicitly for this exactly solvable model.