  A nonlinear flag is a finite sequence of nested closed submanifolds. We study
the geometry of Frechet manifolds of nonlinear flags, in this way generalizing
the nonlinear Grassmannians. As an application we describe a class of coadjoint
orbits of the group of Hamiltonian diffeomorphisms that consist of nested
symplectic submanifolds, i.e., symplectic nonlinear flags.
