  Using the technique of spectral decomposition, we investigated the late-time
tails of massless and massive coupled scalar fields in the background of a
black hole with a global monopole. We found that due to existence of the
coupling between the scalar and gravitational fields, the massless scalar field
decay faster at timelike infinity $i_+$, and so does the massive one in the
intermediate late time. But the asymptotically late-time tail for the massive
scalar field is not affected and its decay rate still is $t^{-5/6}$.
