  We construct the all loop effective action for WZW models perturbed by
current-bilinear terms of the type $J_+J_- $, $J_+J_+ $ and $J_-J_- $, the last
two of which explicitly break Lorentz invariance. For isotropic couplings we
prove integrability. For the case in which only the first two terms are present
we identify a non-perturbative symmetry of the effective action and we compute
the exact beta-functions. These become identically zero outside a bounded
region in the parametric space.
