  We study quantum aspects of the recently constructed doubly lambda-deformed
sigma-models representing the effective action of two WZW models interacting
via current bilinears. We show that although the exact beta-functions and
current anomalous dimensions are identical to those of the lambda-deformed
models, this is not true for the anomalous dimensions of generic primary field
operators in accordance with the fact that the two models differ drastically.
Our proofs involve CFT arguments, as well as effective sigma-model action and
gravity calculations.
