  We give a detailed study of the critical points of the potentials of the
simplest non-trivial N=2 gauged Yang-Mills/Einstein supergravity theories with
tensor multiplets. The scalar field target space of these examples is
SO(1,1)XSO(2,1)/SO(2). The possible gauge groups are SO(2)XU(1)_R and
SO(1,1)XU(1)_R, where U(1)_R is a subgroup of the R-symmetry group SU(2)_R, and
SO(2) and SO(1,1) are subgroups of the isometry group of the scalar manifold.
The scalar potentials of these theories consist of a contribution from the
U(1)_R gauging and a contribution that is due to the presence of the tensor
fields. We find that the latter contribution can change the form of the
supersymmetric extrema from maxima to saddle points. In addition, it leads to
novel critical points not present in the corresponding gauged
Yang-Mills/Einstein supergravity theories without the tensor multiplets. For
the SO(2)XU(1)_R gauged theory these novel critical points correspond to
anti-de Sitter ground states. For the non-compact SO(1,1)XU(1)_R gauging, the
novel ground states are de Sitter. The analysis of the critical points of the
potential carries over in a straightforward manner to the generic family of N=2
gauged Yang-Mills/Einstein supergravity theories coupled to tensor multiplets
whose scalar manifolds are of the form SO(1,1)XSO(n-1,1)/SO(n-1).
