  We investigate the effect of (Curvature)^2-terms on N=1 and N=2 supergravity
in three dimensions. We use the off-shell component fields (e_\mu{}^m,
\psi_\mu, S) for N=1 and (e_\mu{}^m, \psi_\mu, \psi_\mu^*, A_\mu, B, B^*) for
N=2 supergravity. The S, A_\mu and B are respectively a real scalar, a real
vector and a complex scalar auxiliary fields. Both for N=1 and N=2, only two
invariant actions for (Curvature)^2-terms exist, while only the actions with
(Scalar Curvature)^2 are free of negative energy ghosts. Interestingly, the
originally non-physical graviton and gravitino fields start propagating,
together with the scalar field S for the N=1 case, or the complex scalar B and
the longitudinal component \partial_\mu A^\mu for N=2. These new propagating
fields form two new physical massive supermultiplets of spins (1/2,0) with 2 x
(1+1) degrees of freedom for the N=1 case, and two physical massive N=2
supermultiplets of spins (1/2,1/2,0,0) with 2 x (2+2) degrees of freedom for
the N=2 case.
