  Let $H$ be a Hopf algebra and $\mathcal{LR}(H)$ the category of
Yetter-Drinfel'd-Long bimodules over $H$. We first give sufficient and
necessary conditions for $\mathcal{LR}(H)$ to be symmetry and pseudosymmetry,
respectively. We then introduce the definition of $u$-condition in
$\mathcal{LR}(H)$ and discuss the relation between the $u$-condition and the
symmetry of $\mathcal{LR}(H)$. Finally, we show that $\mathcal{LR}(H)$ over a
triangular (cotriangular, resp.) Hopf algebra contains a rich symmetric
subcategory.
