  We consider the change-point problem for the marginal distribution of
subordinated Gaussian processes that exhibit long-range dependence. The
asymptotic distributions of Kolmogorov-Smirnov- and Cram\'{e}r-von Mises type
statistics are investigated under local alternatives. By doing so we are able
to compute the asymptotic relative efficiency of the mentioned tests and the
CUSUM test. In the special case of a mean-shift in Gaussian data it is always
$1$. Moreover our theory covers the scenario where the Hermite rank of the
underlying process changes.
  In a small simulation study we show that the theoretical findings carry over
to the finite sample performance of the tests.
