  We construct a family $I_{n_{\eps}}(f)_{t}$ of continuous stochastic
processes that converges in the sense of finite dimensional distributions to a
multiple Wiener-It\^o integral $I_{n}^{H}(f1^{\otimes n}_{[0,t]})$ with respect
to the fractional Brownian motion. We assume that $H>{1/2}$ and we prove our
approximation result for the integrands $f$ in a rather general class.
