  We perform a generalization of the geometrical approach to describing
extended objects for studying the doubly supersymmetric twistor--like
formulation of super--p--branes. Some basic features of embedding world
supersurface into target superspace specified by a geometrodynamical condition
are considered. It is shown that the main attributes of the geometrical
approach, such as the second fundamental form and extrinsic torsion of the
embedded surface, and the Codazzi, Gauss and Ricci equations, have their doubly
supersymmetric counterparts. At the same time the embedding of supersurface
into target superspace has its particular features. For instance, the embedding
may cause more rigid restrictions on the geometrical properties of the
supersurface. This is demonstrated with the examples of an N=1 twistor--like
supermembrane in D=11 and type II superstrings in D=10, where the
geometrodynamical condition causes the embedded supersurface to be minimal and
puts the theories on the mass shell.
