  In this paper, we consider U-statistics whose data is a strictly stationary
sequence which can be expressed as a functional of an i.i.d. one. We establish
a strong law of large numbers, a bounded law of the iterated logarithms and a
central limit theorem under a dependence condition. The main ingredients for
the proof are an approximation by U-statistics whose data is a functional of
$\ell$ i.i.d. random variables and an analogue of the Hoeffding's decomposition
for U-statistics of this type.
