  We consider sequences of additive functionals of difference approximations
for uniformly non-degenerate multidimensional diffusions. The conditions are
given, sufficient for such a sequence to converge weakly to a W-functional of
the limiting process. The class of the W-functionals, that can be obtained as
the limiting ones, is completely described in the terms of the associated
W-measures, and coincides with the class of the functionals that are regular
w.r.t. the phase variable.
