  We generalize the geometrical formulation of Wilson loops recently introduced
in arXiv:2003.01729v2 to the description of Wilson Surfaces. For N=(2,0) theory
in six dimensions, we provide an explicit derivation of BPS Wilson Surfaces
with non-trivial coupling to scalars, together with their manifestly
supersymmetric version. We derive explicit conditions which allow to classify
these operators in terms of the number of preserved supercharges. We also
discuss kappa-symmetry and prove that BPS conditions in six dimensions arise
from kappa-symmetry invariance in eleven dimensions. Finally, we discuss
super-Wilson Surfaces - and higher dimensional operators - as objects charged
under global $p$-form (super)symmetries generated by tensorial supercurrents.
To this end, the construction of conserved supercurrents in supermanifolds and
of the corresponding conserved charges is developed in details.
