Closed super (p + 2)-forms in target superspace are relevant for the c
onstruction of the usual super p-brane actions. Here we construct clos
ed super (p + 1)-forms on a world-volume superspace. They are built ou
t of the pull-backs of the Kalb-Ramond super (p + 1)-form and its curv
ature. We propose a twistor-like formulation of a class of super p-bra
nes which crucially depends on the existence of these closed super (p
+ 1)-forms.