  The general solutions in the models of closed and open superstring and super
p-branes with exotic fractions of the N=1 supersymmetry are considered and the
spontaneously broken character of the $OSp(1,2M)$ symmetry of the models is
established. It is shown that extending these models by Wess-Zumino terms
generates the Dirichlet boundary conditions for superstring and super p-branes.
Using the generalized Wess-Zumino terms new $OSp(1,2M)$ invariant super p-brane
and Dp-brane-like actions preserving $\frac{M-1}{M}$ fraction of supersymmetry
are proposed. For M=32 these models suggest new superbrane vacua of M-theory
preserving 31 from 32 global supersymmetries.
