Let G be a classical group preserving a sesquilinear form on a vector space V
over R or C. Let Gr(r) be the Grassmannian of isotropic r-dimensional
subspaces. Let H = (G1,G2) be a symmetric subgroup of G. In this paper, we give
a parametrization of H-orbits on Gr(r) in terms of dimensions of various
subspaces. The main result of this paper is the determination of the H
homogeneous structure and the dimension of each orbit. Consequently, we find
all the open orbits. We also treat H-orbits of Gr(r) for symplectic and
orthogonal groups over an algebraic closed field with characteristic not equal
to 2.