  We give a preliminary discussion of how the addition of extra coordinates in
M-theory, which together with the original ones parametrise a U-fold, can serve
as a tool for formulating brane dynamics with manifest U-duality. The redundant
degrees of freedom are removed by generalised self-duality constraints or
calibration conditions made possible by the algebraic structure of U-duality.
This is the written version of an invited talk at the 7th International
Workshop "Supersymmetries and Quantum Symmetries", Dubna, July 30-August 4,
2007.
