  Type II string theory or M-theory contains a broad spectrum of gauge
potentials. In addition to the standard $p$-form potentials, various
mixed-symmetry potentials have been predicted, which may couple to exotic
branes with non-standard tensions. Together with $p$-forms, mixed-symmetry
potentials turn out to be essential to build the multiplets of the U-duality
symmetry in each dimension. In this paper, we systematically determine the set
of mixed-symmetry potentials and exotic branes on the basis of the $E_{11}$
conjecture. We also study the decompositions of U-duality multiplets into
T-duality multiplets and determine which mixed-symmetry tensors are contained
in each of the U-/T-duality multiplets.
