We derive the complete orbit of boundary conditions for supergravity models
which is closed under the action of all local symmetries of these models, and
which eliminates spurious field equations on the boundary. We show that the
Gibbons-Hawking boundary conditions break local supersymmetry if one imposes
local boundary conditions on all fields. Nonlocal boundary conditions are not
ruled out. We extend our analysis to BRST symmetry and to the Hamiltonian
formulation of these models.Comment: 37 pages, v2: references added, v3: misprint correcte