A generalized dilaton action is considered of which the standard dilat
on black hole and spherically reduced gravity are particular cases. Th
e Arnowitt-Deser-Misner (ADM) and the Bondi-Sachs (BS) mass are calcul
ated. Special attention is paid to both the asymptotic conditions for
the metric as well as for the reference spacetime. For the latter one
we suggest a modified expression thereby obtaining a new definition of
energy. Depending on the parameters of the model the Hawking radiatio
n behaves like a positive or negative power of the mass.