  This thesis is devoted to the study of three problems on the
Wess-Zumino-Witten (WZW) and Chern-Simons (CS) supergravity theories in the
Hamiltonian framework: 1) The two-dimensional super WZW model coupled to
supergravity is constructed. The canonical representation of Kac-Moody algebra
is extended to the super Kac-Moody and Virasoro algebras. Then, the canonical
action is constructed, invariant under local supersymmetry transformations. The
metric tensor and Rarita-Schwinger fields emerge as Lagrange multipliers of the
components of the super energy-momentum tensor. 2) In higher dimensions, CS
theories are irregular systems, that is, they have constraints which are
functionally dependent in some sectors of phase space. In these cases, the
standard Dirac procedure must be redefined, as it is shown in the simplified
case of finite number of degrees of freedom. Irregular systems fall into two
classes depending on their behavior in the vicinity of the constraint surface.
In one case, it is possible to regularize the system without ambiguities, while
in the other, regularization is not always possible and the Hamiltonian and
Lagrangian descriptions may be dynamically inequivalent. Irregularities have
important consequences in the linearized approximation of nonlinear theories.
3) The dynamics of CS supergravity theory in D=5, based on the supersymmetric
extension of the AdS algebra, su(2,2|4), is analyzed. A class of backgrounds is
found, providing a regular and generic effective theory. Some of these
backgrounds are shown to be BPS states. The charges for the simplest choice of
asymptotic conditions are obtained, and they satisfy a supersymmetric extension
of the classical WZW(4) algebra, associated to su(2,2|4).
