  We generalize a family of Lagrangians with values in the Poincar\'e group
ISO(d-1,1), which contain the description of spinning strings in flat (d-1)+1
dimensions, by including symmetric terms in the world-sheet coordinates. Then,
by promoting a subgroup H=R^n, n less than or equal to d, which acts
invariantly from the left on the element of ISO(d-1,1), to a gauge symmetry of
the action, we obtain a family of sigma-models. They describe bosonic strings
moving in (generally) curved, and in some cases degenerate, space-times with an
axion field. Further, the space-times of the effective theory admit in general
T-dual geometries. We give explicit results for two non degenerate cases.
