  We prove that the doubly lambda-deformed sigma-models, which include
integrable cases, are canonically equivalent to the sum of two single
lambda-deformed models. This explains the equality of the exact beta-functions
and current anomalous dimensions of the doubly lambda-deformed sigma-models to
those of two single lambda-deformed models. Our proof is based upon agreement
of their Hamiltonian densities and of their canonical structure. Subsequently,
we show that it is possible to take a well defined non-Abelian type limit of
the doubly-deformed action. Last, but not least, by extending the above, we
construct multi-matrix integrable deformations of an arbitrary number of WZW
models.
