  Closed super (p+2)-forms in target superspace are relevant for the
construction of the usual super p-brane actions. Here we construct closed super
(p+1)-forms on a {\it worldvolume superspace}. They are built out of the
pull-backs of the Kalb-Ramond super (p+1)-form and its curvature. We propose a
twistor-like formulation of a class of super p-branes which crucially depends
on the existence of these closed super (p+1)-forms.
