  A procedure is developed for constructing deformations of integrable
sigma-models which are themselves classically integrable. When applied to the
principal chiral model on any compact Lie group F, one recovers the Yang-Baxter
sigma-model introduced a few years ago by C. Klimcik. In the case of the
symmetric space sigma-model on F/G we obtain a new one-parameter family of
integrable sigma-models. The actions of these models correspond to a
deformation of the target space geometry and include a torsion term. An
interesting feature of the construction is the q-deformation of the symmetry
corresponding to left multiplication in the original models, which becomes
replaced by a classical q-deformed Poisson-Hopf algebra. Another noteworthy
aspect of the deformation in the coset sigma-model case is that it interpolates
between a compact and a non-compact symmetric space. This is exemplified in the
case of the SU(2)/U(1) coset sigma-model which interpolates all the way to the
SU(1,1)/U(1) coset sigma-model.
