  The R+S^2 theories of gravity, where S^2 denotes the quadratic torsion terms,
are analyzed under three cases. In the first two cases, the matter fields are
described by two different spin fluids which are not homogeneous and isotropic.
In the third case, a homogeneous and isotropic torsion field is used. It is
found that under all the three cases, the R+S^2 theories may avert the big-bang
singularity of the Robertson--Walker universe, with three corresponding
constraints on the parameters.
