Dehling and Taqqu established the weak convergence of the empirical pr
ocess for a long-range dependent stationary sequence under Gaussian su
bordination. We show that the corresponding density process, based on
kernel estimators of the marginal density, converges weakly with the s
ame normalization to the derivative of their limiting process. The phe
nomenon, which carries on for higher derivatives and for functional la
ws of the iterated logarithm, is in contrast with independent or weakl
y dependent situations, where the density process cannot be tight in t
he usual function spaces with supremum distances.