Let Xn=∑∞i=1aiɛn−i, where the ɛi are i.i.d. with mean 0 and at least finite second moment, and the ai are assumed to satisfy |ai|=O(i−β) with β>1/2. When 1/2<β<1, Xn is usually called a long-range dependent or long-memory process. For a certain class of Borel functions K(x1, …, xd+1), d≥0, from ${\mathcal{R}}^{d+1}$ to $\mathcal{R}$ , which includes indicator functions and polynomials, the stationary sequence K(Xn, Xn+1, …, Xn+d) is considered. By developing a finite orthogonal expansion of K(Xn, …, Xn+d), the Berry–Esseen type bounds for the normalized sum $Q_{N}/\sqrt{N}$ , QN=∑Nn=1(K(Xn, …, Xn+d)−EK(Xn, …, Xn+d)) are obtained when $Q_{N}/\sqrt{N}$ obeys the central limit theorem with positive limiting variance.