For short memory processes nonparametric estimation of quantile functions was considered in Abberger (1996, 1997). Ghosh et. al (1997) consider the kernel estimaton of these functions for suitable transformations of an underlying Gaussian process with long memory. In this paper we consider similar processes, however the underlying Gaussian process is assumed to have serial correlations which decay fast so that the sum of all correlations is finite. We prove the consistency of the kernel estimates of distribution functions which are inverted to obtain consistent estimates of the quantiles. We also discuss a smoother estimate of the quantiles and illustrate the procedure by an application to a precipitation time series from Switzerland.