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We extend the covariant canonical formalism recently discussed in ref. [1] togeometric theories coupled to both bosonic and fermionic $p$-forms. This allowsa covariant hamiltonian treatment of supergravity theories. As examples wepresent the covariant hamiltonian formulation for $d=3$ anti-De Sittersupergravity and for the "new minimal" $d=4$, $N=1$ supergravity (with $1$-formand $2$-form auxiliary fields). Form-Poisson brackets and form-Dirac bracketsare defined, and used to find the form-canonical generators of all gaugesymmetries via an algorithmic procedure.

Covariant hamiltonian for supergravity in $d=3$ and $d=4$