  Hovey introduced a $k$-cordial labeling of graphs as a generalization both of
harmonious and cordial labelings. He proved that all tress are $k$-cordial for
$k \in \{1,...,5\}$ and he conjectured that all trees are $k$-cordial for all
$k$. \indent We consider a corresponding problem for hypergraphs, namely, we
show that $p$-uniform hypertrees are $k$-cordial for certain values of $k$.
