  We establish nonuniform Berry-Esseen (B-E) bounds for Studentized
U-statistics of the rate $1/\sqrt{n}$ under a third-moment assumption, which
covers the t-statistic that corresponds to a kernel of degree $1$ as a special
case. While an interesting data example raised by Novak (2005) can show that
the form of the nonuniform bound for standardized U-statistics is actually
invalid for their Studentized counterparts, our main results suggest that, the
validity of such a bound can be restored by minimally augmenting it with an
additive correction term that decays exponentially in $n$. To our best
knowledge, this is the first time that valid nonuniform B-E bounds for
Studentized U-statistics have appeared in the literature.
