  The Lagrangian formulation of classical field theories and in particular
general relativity leads to a coordinate-free, fully covariant analysis of
these constrained systems. This paper applies multisymplectic techniques to
obtain the analysis of Palatini and self-dual gravity theories as constrained
systems, which have been studied so far in the Hamiltonian formalism. The
constraint equations are derived while paying attention to boundary terms, and
the Hamiltonian constraint turns out to be linear in the multimomenta. The
equivalence with Ashtekar's formalism is also established. The whole constraint
analysis, however, remains covariant in that the multimomentum map is evaluated
on {\it any} spacelike hypersurface. This study is motivated by the
non-perturbative quantization program of general relativity.
