  In this paper, we study Kaplan-Meier V- and U-statistics respectively defined
as $\theta(\widehat{F}_n)=\sum_{i,j}K(X_{[i:n]},X_{[j:n]})W_iW_j$ and
$\theta_U(\widehat{F}_n)=\sum_{i\neq j}K(X_{[i:n]},X_{[j:n]})W_iW_j/\sum_{i\neq
j}W_iW_j$, where $\widehat{F}_n$ is the Kaplan-Meier estimator,
$\{W_1,\ldots,W_n\}$ are the Kaplan-Meier weights and $K:(0,\infty)^2\to\mathbb
R$ is a symmetric kernel. As in the canonical setting of uncensored data, we
differentiate between two asymptotic behaviours for $\theta(\widehat{F}_n)$ and
$\theta_U(\widehat{F}_n)$. Additionally, we derive an asymptotic canonical
V-statistic representation of the Kaplan-Meier V- and U-statistics. By using
this representation we study properties of the asymptotic distribution.
Applications to hypothesis testing are given.
