  Starting with the 2+1 Einstein--Maxwell--Dilaton system with a cosmological
constant and assuming two commuting Killing symmetries we derive the
corresponding $1+0 \sigma$--model. It is shown that, for general values of the
coupling parameters, the $T$--duality group is $SL(2,R)$, which coincides with
the group of linear coordinate transformations along the Killing orbits. This
duality, along with a suitable parameter choice, is applied to obtain some new
spinning solutions in the alternative gravity theories: Einstein--Maxwell,
Brans--Dicke and Einstein--Maxwell--Dilaton.
