  This paper analyzes the limit properties of the empirical process of
$\alpha$-stable random variables with long range dependence. The
$\alpha$-stable random variables are constructed by non-linear transformations
of bivariate sequences of strongly dependent gaussian processes. The approach
followed allows an analysis of the empirical process by means of expansions in
terms of bivariate Hermite polynomials for the full range $0<\alpha<2$. A weak
uniform reduction principle is provided and it is shown that the limiting
process is gaussian. The results of the paper different substantailly from
those available for empirical processes obtained by stable moving averages with
long memory. An application to goodness-of-fit testing is discussed.
