  Here we show that the phenomenon of arbitrarily long-lived quasinormal modes
(called quasiresonances) of a massive scalar field in the vicinity of a black
hole is not an artifact of the test field approximation, but takes place also
when the (derivative) coupling of a scalar field with the Einstein tensor is
taken into consideration. We observe that at large coupling and high multipole
numbers, the growing modes appear in the spectrum, which are responsible for
the eikonal instability of the field. For small coupling, when the
configuration is stable, there appear the purely imaginary quasinormal modes
which are nonperturbative in the coupling constant. At the sufficiently small
coupling the nonminimal scalar field is stable and the asymptotic late-time
tails are not affected by the coupling term. The accurate calculations of
quasinormal frequencies for a massive scalar field with the derivative coupling
in the Reissner-Nordstr\"om black-hole background are performed with the help
of Frobenius method, time-domain integration and WKB expansion.
