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<P ALIGN=RIGHT><FONT SIZE=+4>41</FONT><P>
Herold Dehling
Murad S. Taqqu
be a stationary, mean-zero Gaussian process with
covariances 
satisfying 
and 
where D is small and L is slowly varying at infinity.
Consider the two-parameter empirical process 
for
,
where G is any measurable function. Non-central limit theorems are
obtained for 
and they are used to derive the asymptotic behavior of some suitably normalized von Mises statistics
and U-statistics based on the 
's.
The limiting processes are structurally different
from those encountered in the i.i.d. case.