  We adress ourselves the question of the quantum equivalence of non abelian
dualised $\si$-models on the simple example of the T-dualised $SU(2)
\si$-model. This theory is classically canonically equivalent to the standard
chiral $SU(2) \si$-model. It is known that the equivalence also holds at the
first order in perturbations with the same $\be$ functions. However, this model
has been claimed to be non-renormalisable at the two-loop order. The aim of the
present work is the proof that it is - at least up to this order - still
possible to define a correct quantum theory. Its target space metric being only
modified in a finite manner, all divergences are reabsorbed into coupling and
fields (infinite) renormalisations.
