Extended super self-dual systems have a structure reminiscent of a
``matreoshka''. For instance, solutions for N=0 are embedded in solutions for
N=1, which are in turn embedded in solutions for N=2, and so on. Consequences
of this phenomenon are explored. In particular, we present an explicit
construction of local solutions of the higher-N super self-duality equations
starting from any N=0 self-dual solution. Our construction uses N=0 solution
data to produce N=1 solution data, which in turn yields N=2 solution data, and
so on; each stage introducing a dependence of the solution on sufficiently many
additional arbitrary functions to yield the most general supersymmetric
solution having the initial N=0 solution as the helicity +1 component. The
problem of finding the general local solution of the N>0 super self-duality
equations therefore reduces to finding the general solution of the usual (N=0)
self-duality equations. Another consequence of the matreoshka phenomenon is the
vanishing of many conserved currents, including the supercurrents, for super
self-dual systems.Comment: 19 pages, Bonn-HE-93-2