  We study the decay of Dirac and massive scalar fields at asymptotically late
times in the background of the charged asymptotically de Sitter dilatonic black
holes. It is shown that the asymptotic decay is exponential and oscillatory for
large and intermediate mass of the field, while for zero and small mass it is
pure exponential without oscillations. This reflects the dominance of
quasinormal modes of the empty de Sitter spacetime at asymptotically late
times. We also show that the earlier WKB calculation of the massive scalar
field spectrum %[S. Fernando, Gen.Rel.Grav. 48 (2016) 3, 24] does not allow one
to find the fundamental mode with reasonable accuracy.
