  Let $X_n=\sum_{i=1}^{\infty}a_i\epsilon_{n-i}$, where the $\epsilon_i$ are
i.i.d. with mean 0 and at least finite second moment, and the $a_i$ are assumed
to satisfy $|a_i|=O(i^{-\beta})$ with $\beta >1/2$. When $1/2<\beta<1$, $X_n$
is usually called a long-range dependent or long-memory process. For a certain
class of Borel functions $K(x_1,...,x_{d+1})$, $d\ge0$, from
${\mathcal{R}}^{d+1}$ to $\mathcal{R}$, which includes indicator functions and
polynomials, the stationary sequence $K(X_n,X_{n+1},...,X_{n+d})$ is
considered. By developing a finite orthogonal expansion of
$K(X_n,...,X_{n+d})$, the Berry--Esseen type bounds for the normalized sum
$Q_N/\sqrt{N},Q_N=\sum_{n=1}^N(K(X_
n,...,X_{n+d})-\mathrm{E}K(X_n,...,X_{n+d}))$ are obtained when $Q_N/\sqrt{N}$
obeys the central limit theorem with positive limiting variance.
