  We generalise the notion of the Tate-Shafarevich group of an elliptic K3
surface with a section to the Tate-Shafarevich group of a K3 surface endowed
with a linear system. The construction, which uses Grothendieck's special
Brauer group, provides an efficient way to deal with moduli spaces of twisted
sheaves supported on curves in a K3 surface.
