The main subject of this thesis is the study of the N = 4 supergravity theories. Superspace geometry is used to search for all N = 4 supergravities with at least SO(4) global symmetry. It is found that the general solution to the unconstrained Bianchi Identities, with the field content of N = 4 supergravity, are equivalent to the known SO(4) and SU(4) supergravities up to field redefinitions. Therefore the field content determines uniquely the N = 4 theories and further constraints are not necessary.
The SO(4) supergravity is gauged with two coupling constants and a new theory with positive cosmological constant and spontaneous breaking of the four supersymmetries is found. The presence of scalar fields in the kinetic term of the vectors is seen to make the values of the physical gauge coupling constants depend on the choice of vacuum.
