  A lot of developments made during the last years show that Kac-Moody algebras
play an important role in the algebraic structure of some supergravity
theories. These algebras would generate infinite-dimensional symmetry groups.
The possible existence of such symmetries have motivated the reformulation of
these theories as non-linear sigma-models based on the Kac-Moody symmetry
groups. Such models are constructed in terms of an infinite number of fields
parametrizing the generators of the corresponding algebra. If these conjectured
symmetries are indeed actual symmetries of certain supergravity theories, a
meaningful question to elucidate will be the interpretation of this infinite
tower of fields. Another substantial problem is to find the correspondence
between the sigma-models, which are explicitly invariant under the conjectured
symmetries, and these corresponding space-time theories. The subject of this
thesis is to address these questions in certain cases.
