  In this paper we realize the dynamical categories introduced in our previous
paper as categories of modules over bialgebroids; we study the bialgebroids
arising in this way. We define quasitriangular structure on bialgebroids and
present examples of quasitriangular bialgebroids related to the dynamical
categories. We show that dynamical twists over an arbitrary base give rise to
bialgebroid twists.
  We prove that the classical dynamical r-matrices over an arbitrary base
manifold are in one-to-one correspondence with a special class of coboundary
Lie bialgebroids.
