Twistor-like Formulation of Super p-Branes

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.